Let (M,G) be a finite global quotient, that is, a finite set M with an action by a finite group G. In this note, we classify all bicovariant first order differential calculi (FODCs) over the weak Hopf algebra k(G⋉M) ≃ k[G⋉M ], where G⋉M is the action groupoid associated to (M,G), and k[G ⋉M ] is the groupoid algebra of G ⋉ M . Specifically, we prove a necessary and sufficient condition for a FODC over k(G ⋉ M) to be bicovariant and then show that the isomorphism classes of bicovariant FODCs over k(G⋉M) are in one-to-one correspondence with subsets of a certain quotient space.
{"title":"Bicovariant differential calculi for finite global quotients","authors":"D. Pham","doi":"10.3336/gm.54.2.10","DOIUrl":"https://doi.org/10.3336/gm.54.2.10","url":null,"abstract":"Let (M,G) be a finite global quotient, that is, a finite set M with an action by a finite group G. In this note, we classify all bicovariant first order differential calculi (FODCs) over the weak Hopf algebra k(G⋉M) ≃ k[G⋉M ], where G⋉M is the action groupoid associated to (M,G), and k[G ⋉M ] is the groupoid algebra of G ⋉ M . Specifically, we prove a necessary and sufficient condition for a FODC over k(G ⋉ M) to be bicovariant and then show that the isomorphism classes of bicovariant FODCs over k(G⋉M) are in one-to-one correspondence with subsets of a certain quotient space.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74612356","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}
In this paper, we study integral points and generators on quartic curves of the forms u2±v4 = m for a nonzero integer m. The main results assert that certain integral points on the curves can be extended to bases for the Mordell-Weil groups of the elliptic curves attached to the quartic curves in the cases where the Mordell-Weil ranks are at most two. As corollaries, we explicitly describe the integral points on the quartic curves in each case where the ranks are one and two.
{"title":"Generators and integral points on certain quartic curves","authors":"Y. Fujita, T. Nara","doi":"10.3336/gm.54.2.04","DOIUrl":"https://doi.org/10.3336/gm.54.2.04","url":null,"abstract":"In this paper, we study integral points and generators on quartic curves of the forms u2±v4 = m for a nonzero integer m. The main results assert that certain integral points on the curves can be extended to bases for the Mordell-Weil groups of the elliptic curves attached to the quartic curves in the cases where the Mordell-Weil ranks are at most two. As corollaries, we explicitly describe the integral points on the quartic curves in each case where the ranks are one and two.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82493736","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}
We prove that the minimally displaced set of a relatively irreducible automorphism of a free splitting, situated in a deformation space, is uniformly locally finite. The minimally displaced set coincides with the train track points for an irreducible automorphism. We develop the theory in a general setting of deformation spaces of free products, having in mind the study of the action of reducible automorphisms of a free group on the simplicial bordification of Outer Space. For instance, a reducible automorphism will have invariant free factors, act on the corresponding stratum of the bordification, and in that deformation space it may be irreducible (sometimes this is referred as relative irreducibility).
{"title":"The minimally displaced set of an irreducible automorphism is locally finite","authors":"S. Francaviglia, A. Martino, Dionysios Syrigos","doi":"10.3336/gm.55.2.09","DOIUrl":"https://doi.org/10.3336/gm.55.2.09","url":null,"abstract":"We prove that the minimally displaced set of a relatively irreducible automorphism of a free splitting, situated in a deformation space, is uniformly locally finite. The minimally displaced set coincides with the train track points for an irreducible automorphism. We develop the theory in a general setting of deformation spaces of free products, having in mind the study of the action of reducible automorphisms of a free group on the simplicial bordification of Outer Space. For instance, a reducible automorphism will have invariant free factors, act on the corresponding stratum of the bordification, and in that deformation space it may be irreducible (sometimes this is referred as relative irreducibility).","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84660683","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}
The paper extends the study of the modified Borwein method for the calculation of the Riemann zeta-function. It presents an alternative perspective on the proof of a local limit theorem for coefficients of the method. The new approach is based on the connection with the limit theorem applied to asymptotic enumeration.
{"title":"A local limit theorem for coefficients of modified Borwein's method","authors":"I. Belovas","doi":"10.3336/gm.54.1.01","DOIUrl":"https://doi.org/10.3336/gm.54.1.01","url":null,"abstract":"The paper extends the study of the modified Borwein method for the calculation of the Riemann zeta-function. It presents an alternative perspective on the proof of a local limit theorem for coefficients of the method. The new approach is based on the connection with the limit theorem applied to asymptotic enumeration.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84585984","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}
Let Gn denote either symplectic or odd special orthogonal group of rank n over a non-archimedean local field F . We provide an explicit description of the Aubert duals of irreducible representations of Gn which occur in the first inductive step in the realization of discrete series representations starting from the strongly positive ones. Our results might serve as a pattern for determination of Aubert duals of general discrete series of Gn and should produce an interesting part of the unitary dual of this group. Furthermore, we obtain an explicit form of some representations which are known to be unitarizable.
{"title":"Aubert duals of discrete series: the first inductive step","authors":"Ivan Matić","doi":"10.3336/gm.54.1.07","DOIUrl":"https://doi.org/10.3336/gm.54.1.07","url":null,"abstract":"Let Gn denote either symplectic or odd special orthogonal group of rank n over a non-archimedean local field F . We provide an explicit description of the Aubert duals of irreducible representations of Gn which occur in the first inductive step in the realization of discrete series representations starting from the strongly positive ones. Our results might serve as a pattern for determination of Aubert duals of general discrete series of Gn and should produce an interesting part of the unitary dual of this group. Furthermore, we obtain an explicit form of some representations which are known to be unitarizable.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75333271","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}
Time decay estimates are derived for solutions of some initial value problems of wave propagation, based on the method of stationary phase. Solutions to three dimensional wave equation in wedges and one dimensional wave equation with a constant potential are shown to decay like t−1 and t−1/2, respectively. Dependencies of the results on initial data and physical implications are discussed.
{"title":"Time decay estimates for wave equations with transmission and boundary conditions","authors":"K. Mihalinci'c","doi":"10.3336/GM.54.1.08","DOIUrl":"https://doi.org/10.3336/GM.54.1.08","url":null,"abstract":"Time decay estimates are derived for solutions of some initial value problems of wave propagation, based on the method of stationary phase. Solutions to three dimensional wave equation in wedges and one dimensional wave equation with a constant potential are shown to decay like t−1 and t−1/2, respectively. Dependencies of the results on initial data and physical implications are discussed.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79280863","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":"Diophantine m-tuples with the property D(n)","authors":"Riley Becker, M. Murty","doi":"10.3336/gm.54.1.05","DOIUrl":"https://doi.org/10.3336/gm.54.1.05","url":null,"abstract":"","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81252823","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}
In this note we show that many subgroups of mapping class groups of infinite-type surfaces without boundary have trivial centers, including all normal subgroups. Using similar techniques, we show that every nontrivial normal subgroup of a big mapping class group contains a nonabelian free group. In contrast, we show that no big mapping class group satisfies the strong Tits alternative enjoyed by finite-type mapping class groups. We also give examples of big mapping class groups that fail to satisfy even the classical Tits alternative and give a proof that every countable group appears as a subgroup of some big mapping class group.
{"title":"Centers of subgroups of big mapping class groups and the Tits alternative","authors":"Justin Lanier, Marissa Loving","doi":"10.3336/gm.55.1.07","DOIUrl":"https://doi.org/10.3336/gm.55.1.07","url":null,"abstract":"In this note we show that many subgroups of mapping class groups of infinite-type surfaces without boundary have trivial centers, including all normal subgroups. Using similar techniques, we show that every nontrivial normal subgroup of a big mapping class group contains a nonabelian free group. In contrast, we show that no big mapping class group satisfies the strong Tits alternative enjoyed by finite-type mapping class groups. We also give examples of big mapping class groups that fail to satisfy even the classical Tits alternative and give a proof that every countable group appears as a subgroup of some big mapping class group.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75621838","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}
Given a set $S$ of elements in a number field $k$, we discuss the existence of planar algebraic curves over $k$ which possess rational points whose $x$-coordinates are exactly the elements of $S$. If the size $|S|$ of $S$ is either $4,5$, or $6$, we exhibit infinite families of (twisted) Edwards curves and (general) Huff curves for which the elements of $S$ are realized as the $x$-coordinates of rational points on these curves. This generalizes earlier work on progressions of certain types on some algebraic curves.
{"title":"Rational sequences on different models of elliptic curves","authors":"Gamze Savacs cCEL.IK, M. Sadek, G. Soydan","doi":"10.3336/gm.54.1.04","DOIUrl":"https://doi.org/10.3336/gm.54.1.04","url":null,"abstract":"Given a set $S$ of elements in a number field $k$, we discuss the existence of planar algebraic curves over $k$ which possess rational points whose $x$-coordinates are exactly the elements of $S$. If the size $|S|$ of $S$ is either $4,5$, or $6$, we exhibit infinite families of (twisted) Edwards curves and (general) Huff curves for which the elements of $S$ are realized as the $x$-coordinates of rational points on these curves. This generalizes earlier work on progressions of certain types on some algebraic curves.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88853354","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}
4101. Describe the p-groups all of whose subgroups of index p, k ∈ {2, 3, 4}, are normal (three problems). Consider in detail the groups of exponent p. 4102. Study the nonabelian p-groups G all of whose maximal abelian subgroups are normal (any two elements of G generate a subgroup of class ≤ 2 so our group is regular if p > 2, by Theorem 7.1(b) in [B1]). Consider in detail the case p = 2. 4103. Find the maximal possible order of the automorphism groups of the groups of maximal class of order p. 4104. Study the non-Dedekindian p-groups covered by nonnormal subgroups. 4105. Study the p-groups G in which the intersection of any two nonincident subgroups, say A and B, of equal order (of different orders) is normal (i) either in A or in B, (ii) in 〈A,B〉. 4106. Study the p-groups G all of whose nonabelian subgroups of equal order are isomorphic (permutable). Consider in detail the case when exp(G) = p.
{"title":"Further research problems and theorems on prime power groups","authors":"Y. Berkovich, Z. Janko","doi":"10.3336/gm.54.1.06","DOIUrl":"https://doi.org/10.3336/gm.54.1.06","url":null,"abstract":"4101. Describe the p-groups all of whose subgroups of index p, k ∈ {2, 3, 4}, are normal (three problems). Consider in detail the groups of exponent p. 4102. Study the nonabelian p-groups G all of whose maximal abelian subgroups are normal (any two elements of G generate a subgroup of class ≤ 2 so our group is regular if p > 2, by Theorem 7.1(b) in [B1]). Consider in detail the case p = 2. 4103. Find the maximal possible order of the automorphism groups of the groups of maximal class of order p. 4104. Study the non-Dedekindian p-groups covered by nonnormal subgroups. 4105. Study the p-groups G in which the intersection of any two nonincident subgroups, say A and B, of equal order (of different orders) is normal (i) either in A or in B, (ii) in 〈A,B〉. 4106. Study the p-groups G all of whose nonabelian subgroups of equal order are isomorphic (permutable). Consider in detail the case when exp(G) = p.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78615014","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：