Pub Date : 2023-03-13DOI: 10.21136/CMJ.2023.0420-22
Yinghua Wang, Xinnian Song, Lei Gao
By properties of Cvetković-Kostić-Varga-type (or, for short, CKV-type) B-matrices, a new class of nonsingular matrices called CKV-type B¯documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$overline{B}$$end{document}-matrices is given, and a new inclusion interval of the real eigenvalues of real matrices is presented. It is shown that the new inclusion interval is sharper than those provided by J. M. Peña (2003), and by H. B. Li et al. (2007). We also propose a direct algorithm for computing the new inclusion interval. Numerical examples are included to illustrate the effectiveness of the obtained results.
{"title":"A new inclusion interval for the real eigenvalues of real matrices","authors":"Yinghua Wang, Xinnian Song, Lei Gao","doi":"10.21136/CMJ.2023.0420-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0420-22","url":null,"abstract":"By properties of Cvetković-Kostić-Varga-type (or, for short, CKV-type) B-matrices, a new class of nonsingular matrices called CKV-type B¯documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$overline{B}$$end{document}-matrices is given, and a new inclusion interval of the real eigenvalues of real matrices is presented. It is shown that the new inclusion interval is sharper than those provided by J. M. Peña (2003), and by H. B. Li et al. (2007). We also propose a direct algorithm for computing the new inclusion interval. Numerical examples are included to illustrate the effectiveness of the obtained results.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"979 - 992"},"PeriodicalIF":0.5,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42804742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-08DOI: 10.21136/CMJ.2023.0322-22
Quan Yang, J. Mehta, S. Kanemitsu
We shall establish an explicit formula for the Davenport series in terms of trivial zeros of the Riemann zeta-function, where by the Davenport series we mean an infinite series involving a PNT (Prime Number Theorem) related to arithmetic function an with the periodic Bernoulli polynomial weight documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$overline{B}_{x}(nx)$$end{document} and PNT arithmetic functions include the von Mangoldt function, Möbius function and Liouville function, etc. The Riesz sum of order 0 or 1 gives the well-known explicit formula for respectively the partial sum or the Riesz sum of order 1 of PNT functions. Then we may reveal the genesis of the Popov explicit formula as the integrated Davenport series with the Riesz sum of order 1 subtracted. The Fourier expansion of the Davenport series is proved to be a consequence of the functional equation, which is referred to as the Davenport expansion. By the explicit formula for the Davenport series, we also prove that the Davenport expansion for the von Mangoldt function is equivalent to the Kummer’s Fourier series up to a formula of Ramanujan and a fortiori is equivalent to the functional equation for the Riemann zeta-function.
We shall establish an explicit formula for the Davenport series in terms of trivial zeros of the Riemann zeta-function, where by the Davenport series we mean an infinite series involving a PNT (Prime Number Theorem) related to arithmetic function an with the periodic Bernoulli polynomial weight documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$overline{B}_{x}(nx)$$end{document} and PNT arithmetic functions include the von Mangoldt function, Möbius function and Liouville function, etc. The Riesz sum of order 0 or 1 gives the well-known explicit formula for respectively the partial sum or the Riesz sum of order 1 of PNT functions. Then we may reveal the genesis of the Popov explicit formula as the integrated Davenport series with the Riesz sum of order 1 subtracted. The Fourier expansion of the Davenport series is proved to be a consequence of the functional equation, which is referred to as the Davenport expansion. By the explicit formula for the Davenport series, we also prove that the Davenport expansion for the von Mangoldt function is equivalent to the Kummer’s Fourier series up to a formula of Ramanujan and a fortiori is equivalent to the functional equation for the Riemann zeta-function.
{"title":"On Popov’s explicit formula and the Davenport expansion","authors":"Quan Yang, J. Mehta, S. Kanemitsu","doi":"10.21136/CMJ.2023.0322-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0322-22","url":null,"abstract":"We shall establish an explicit formula for the Davenport series in terms of trivial zeros of the Riemann zeta-function, where by the Davenport series we mean an infinite series involving a PNT (Prime Number Theorem) related to arithmetic function an with the periodic Bernoulli polynomial weight documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$overline{B}_{x}(nx)$$end{document} and PNT arithmetic functions include the von Mangoldt function, Möbius function and Liouville function, etc. The Riesz sum of order 0 or 1 gives the well-known explicit formula for respectively the partial sum or the Riesz sum of order 1 of PNT functions. Then we may reveal the genesis of the Popov explicit formula as the integrated Davenport series with the Riesz sum of order 1 subtracted. The Fourier expansion of the Davenport series is proved to be a consequence of the functional equation, which is referred to as the Davenport expansion. By the explicit formula for the Davenport series, we also prove that the Davenport expansion for the von Mangoldt function is equivalent to the Kummer’s Fourier series up to a formula of Ramanujan and a fortiori is equivalent to the functional equation for the Riemann zeta-function.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"869 - 883"},"PeriodicalIF":0.5,"publicationDate":"2023-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44847424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-08DOI: 10.21136/CMJ.2023.0027-20
Ruyun Ma, Zhiqian He, Xiaoxiao Su
Let E = {u ∈ C1[0, 1]: u(0) = u(1) = 0}. Let Skv with v = {+, −} denote the set of functions u ∈ E which have exactly k − 1 interior nodal zeros in (0, 1) and vu be positive near 0. We show the existence of S-shaped connected component of Skv-solutions of the problem {(u′1−u′2)′+λa(x)f(u)=0,x∈(0,1),u(0)=u(1)=0,documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$left{ {begin{array}{*{20}{c}} {begin{array}{*{20}{c}} {{{left( {frac{{u'}}{{sqrt {1 - {{u'}^2}} }}} right)}^prime } + lambda a(x)f(u) = 0,}&{x in (0,1)} end{array}} {u(0) = u(1) = 0,;;;;;;;;;;;;;;;;;;;;;;;;;;} end{array}} right.$$end{document} where λ > 0 is a parameter, a ∈ C([0, 1], (0, ∞)). We determine the intervals of parameter λ in which the above problem has one, two or three Skv-solutions. The proofs of the main results are based upon the bifurcation technique.
{"title":"S-shaped component of nodal solutions for problem involving one-dimension mean curvature operator","authors":"Ruyun Ma, Zhiqian He, Xiaoxiao Su","doi":"10.21136/CMJ.2023.0027-20","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0027-20","url":null,"abstract":"Let E = {u ∈ C1[0, 1]: u(0) = u(1) = 0}. Let Skv with v = {+, −} denote the set of functions u ∈ E which have exactly k − 1 interior nodal zeros in (0, 1) and vu be positive near 0. We show the existence of S-shaped connected component of Skv-solutions of the problem {(u′1−u′2)′+λa(x)f(u)=0,x∈(0,1),u(0)=u(1)=0,documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$left{ {begin{array}{*{20}{c}} {begin{array}{*{20}{c}} {{{left( {frac{{u'}}{{sqrt {1 - {{u'}^2}} }}} right)}^prime } + lambda a(x)f(u) = 0,}&{x in (0,1)} end{array}} {u(0) = u(1) = 0,;;;;;;;;;;;;;;;;;;;;;;;;;;} end{array}} right.$$end{document} where λ > 0 is a parameter, a ∈ C([0, 1], (0, ∞)). We determine the intervals of parameter λ in which the above problem has one, two or three Skv-solutions. The proofs of the main results are based upon the bifurcation technique.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"321 - 333"},"PeriodicalIF":0.5,"publicationDate":"2023-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47410279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the divisor function over Piatetski-Shapiro sequences","authors":"Hui Wang, Yu Zhang","doi":"10.21136/CMJ.2023.0205-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0205-22","url":null,"abstract":"Let [x] be an integer part of x and d(n) be the number of positive divisor of n. Inspired by some results of M. Jutila (1987), we prove that for 1<c<65documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$1 < c < {6 over 5}$$end{document}∑n≤xd([nc])=cxlogx+(2γ−c)x+O(xlogx),documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$sumlimits_{n le x} {d([{n^c}]) = cx,log x + (2{rm{gamma }} - c)x + Oleft( {{x over {log x}}} right),} $$end{document} where γ is the Euler constant and [nc] is the Piatetski-Shapiro sequence. This gives an improvement upon the classical result of this problem.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"613 - 620"},"PeriodicalIF":0.5,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44066103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-06DOI: 10.21136/CMJ.2023.0246-22
Hong Wang, Zhongming Tang
Let G=Kn1,n2,…,nrdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$G = {K_{{n_1},{n_2}, ldots ,{n_r}}}$$end{document} be a complete multipartite graph on [n] with n > r > 1 and JG being its binomial edge ideal. It is proved that the Castelnuovo-Mumford regularity reg(JGt) is 2t +1 for any positive integer t.
{"title":"Regularity of powers of binomial edge ideals of complete multipartite graphs","authors":"Hong Wang, Zhongming Tang","doi":"10.21136/CMJ.2023.0246-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0246-22","url":null,"abstract":"Let G=Kn1,n2,…,nrdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$G = {K_{{n_1},{n_2}, ldots ,{n_r}}}$$end{document} be a complete multipartite graph on [n] with n > r > 1 and JG being its binomial edge ideal. It is proved that the Castelnuovo-Mumford regularity reg(JGt) is 2t +1 for any positive integer t.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"793 - 810"},"PeriodicalIF":0.5,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47758397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-14DOI: 10.21136/CMJ.2023.0230-21
Jae‐Myoung Kim
We show the upper and lower bounds of convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under a large initial perturbation.
我们给出了在大的初始扰动下与麦克斯韦方程组相关的三维非牛顿流的强解的收敛速度的上界和下界。
{"title":"Upper and lower convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under large initial perturbation","authors":"Jae‐Myoung Kim","doi":"10.21136/CMJ.2023.0230-21","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0230-21","url":null,"abstract":"We show the upper and lower bounds of convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under a large initial perturbation.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"395 - 413"},"PeriodicalIF":0.5,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49258141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-14DOI: 10.21136/CMJ.2023.0208-22
Qiannan Zhang, Hua Yang
In this paper we study the balanced metrics on some Hartogs triangles of exponent γ ∈ ℤ+, i.e. equipped with a natural Kähler form with where μ = (μ1, …, μn), μi > 0, depending on n parameters. The purpose of this paper is threefold. First, we compute the explicit expression for the weighted Bergman kernel function for (Ωn(γ),g(μ)) and we prove that g(μ) is balanced if and only if μ1 > 1 and γμ1 is an integer, μi are integers such that μi ≽ 2 for all i = 2, …, n − 1, and μn > 1. Second, we prove that g(μ) is Kähler-Einstein if and only if μ1 = μ2 = … = μn = 2λ, where λ is a nonzero constant. Finally, we show that if g(μ) is balanced then (Ωn(γ),g(μ)) admits a Berezin-Engliš quantization.
{"title":"Remarks on the balanced metric on Hartogs triangles with integral exponent","authors":"Qiannan Zhang, Hua Yang","doi":"10.21136/CMJ.2023.0208-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0208-22","url":null,"abstract":"In this paper we study the balanced metrics on some Hartogs triangles of exponent γ ∈ ℤ+, i.e. equipped with a natural Kähler form with where μ = (μ1, …, μn), μi > 0, depending on n parameters. The purpose of this paper is threefold. First, we compute the explicit expression for the weighted Bergman kernel function for (Ωn(γ),g(μ)) and we prove that g(μ) is balanced if and only if μ1 > 1 and γμ1 is an integer, μi are integers such that μi ≽ 2 for all i = 2, …, n − 1, and μn > 1. Second, we prove that g(μ) is Kähler-Einstein if and only if μ1 = μ2 = … = μn = 2λ, where λ is a nonzero constant. Finally, we show that if g(μ) is balanced then (Ωn(γ),g(μ)) admits a Berezin-Engliš quantization.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"633 - 647"},"PeriodicalIF":0.5,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44956671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-08DOI: 10.21136/CMJ.2023.0372-21
Rongmin Zhu, Jiaqun Wei
Let U be a dg-A-module, B the endomorphism dg-algebra of U. We know that if U is a good silting object, then there exist a dg-algebra C and a recollement among the derived categories D(C, d) of C, D(B, d) of B and D(A, d) of A. We investigate the condition under which the induced dg-algebra C is weak nonpositive. In order to deal with both silting and cosilting dg-modules consistently, the notion of weak silting dg-modules is introduced. Thus, similar results for good cosilting dg-modules are obtained. Finally, some applications are given related to good 2-term silting complexes, good tilting complexes and modules.
{"title":"Recollements induced by good (co)silting dg-modules","authors":"Rongmin Zhu, Jiaqun Wei","doi":"10.21136/CMJ.2023.0372-21","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0372-21","url":null,"abstract":"Let U be a dg-A-module, B the endomorphism dg-algebra of U. We know that if U is a good silting object, then there exist a dg-algebra C and a recollement among the derived categories D(C, d) of C, D(B, d) of B and D(A, d) of A. We investigate the condition under which the induced dg-algebra C is weak nonpositive. In order to deal with both silting and cosilting dg-modules consistently, the notion of weak silting dg-modules is introduced. Thus, similar results for good cosilting dg-modules are obtained. Finally, some applications are given related to good 2-term silting complexes, good tilting complexes and modules.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"453 - 473"},"PeriodicalIF":0.5,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43986454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-08DOI: 10.21136/cmj.2023.0235-22
C. M. Cuesta, Xuban Diez
We study the large time behaviour of the solutions of a non-local regularisation of a scalar conservation law. This regularisation is given by a fractional derivative of order $1+alpha$, with $alphain(0,1)$, which is a Riesz-Feller operator. The non-linear flux is given by the locally Lipschitz function $|u|^{q-1}u/q$ for $q>1$. We show that in the sub-critical case, $1
{"title":"Large time behaviour of a conservation law regularised by a Riesz-Feller operator: the sub-critical case","authors":"C. M. Cuesta, Xuban Diez","doi":"10.21136/cmj.2023.0235-22","DOIUrl":"https://doi.org/10.21136/cmj.2023.0235-22","url":null,"abstract":"We study the large time behaviour of the solutions of a non-local regularisation of a scalar conservation law. This regularisation is given by a fractional derivative of order $1+alpha$, with $alphain(0,1)$, which is a Riesz-Feller operator. The non-linear flux is given by the locally Lipschitz function $|u|^{q-1}u/q$ for $q>1$. We show that in the sub-critical case, $1<q<1 +alpha$, the large time behaviour is governed by the unique entropy solution of the scalar conservation law. Our proof adapts the proofs of the analogous results for the local case (where the regularisation is the Laplacian) and, more closely, the ones for the regularisation given by the fractional Laplacian with order larger than one, see Ignat and Stan (2018). The main difference is that our operator is not symmetric and its Fourier symbol is not real. We can also adapt the proof and obtain similar results for general Riesz-Feller operators.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41350628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-07DOI: 10.21136/CMJ.2023.0254-22
Shiou-Yi Lin, Shilin Yang
We investigate the representation theory of the positively based algebra Am,d, which is a generalization of the noncommutative Green algebra of weak Hopf algebra corresponding to the generalized Taft algebra. It turns out that Am,d is of finite representative type if d ⩽ 4, of tame type if d = 5, and of wild type if d ⩾ 6. In the case when d ⩽ 4, all indecomposable representations of Am,d are constructed. Furthermore, their right cell representations as well as left cell representations of Am,d are described.
{"title":"Representations of a class of positively based algebras","authors":"Shiou-Yi Lin, Shilin Yang","doi":"10.21136/CMJ.2023.0254-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0254-22","url":null,"abstract":"We investigate the representation theory of the positively based algebra Am,d, which is a generalization of the noncommutative Green algebra of weak Hopf algebra corresponding to the generalized Taft algebra. It turns out that Am,d is of finite representative type if d ⩽ 4, of tame type if d = 5, and of wild type if d ⩾ 6. In the case when d ⩽ 4, all indecomposable representations of Am,d are constructed. Furthermore, their right cell representations as well as left cell representations of Am,d are described.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"811 - 838"},"PeriodicalIF":0.5,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42046591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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