Pub Date : 2019-03-30DOI: 10.1215/21562261-2022-0028
Daniel Gromada, Moritz Weber
We present an algorithm for approximating linear categories of partitions (of sets). We report on concrete computer experiments based on this algorithm and how we found new examples of compact matrix quantum groups (so called "non-easy" quantum groups) with it. This also led to further theoretical insights regarding the representation theory of such quantum groups. We interpret some of the new categories constructing anticommutative twists of quantum groups.
{"title":"Generating linear categories of partitions","authors":"Daniel Gromada, Moritz Weber","doi":"10.1215/21562261-2022-0028","DOIUrl":"https://doi.org/10.1215/21562261-2022-0028","url":null,"abstract":"We present an algorithm for approximating linear categories of partitions (of sets). We report on concrete computer experiments based on this algorithm and how we found new examples of compact matrix quantum groups (so called \"non-easy\" quantum groups) with it. This also led to further theoretical insights regarding the representation theory of such quantum groups. We interpret some of the new categories constructing anticommutative twists of quantum groups.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43630192","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 : 2019-03-19DOI: 10.1215/21562261-2022-0020
D. Kishimoto, R. Levi
Polyhedral products were defined by Bahri, Bendersky, Cohen and Gitler, to be spaces obtained as unions of certain product spaces indexed by the simplices of an abstract simplicial complex. In this paper we give a very general homotopy theoretic construction of polyhedral products over arbitrary pointed posets. We show that under certain restrictions on the poset $calp$, that include all known cases, the cohomology of the resulting spaces can be computed as an inverse limit over $calp$ of the cohomology of the building blocks. This motivates the definition of an analogous algebraic construction - the polyhedral tensor product. We show that for a large family of posets, the cohomology of the polyhedral product is given by the polyhedral tensor product. We then restrict attention to polyhedral posets, a family of posets that include face posets of simplicial complexes, and simplicial posets, as well as many others. We define the Stanley-Reisner ring of a polyhedral poset and show that, like in the classical cases, these rings occur as the cohomology of certain polyhedral products over the poset in question. For any pointed poset $calp$ we construct a simplicial poset $s(calp)$, and show that if $calp$ is a polyhedral poset then polyhedral products over $calp$ coincide up to homotopy with the corresponding polyhedral products over $s(calp)$.
{"title":"Polyhedral products over finite posets","authors":"D. Kishimoto, R. Levi","doi":"10.1215/21562261-2022-0020","DOIUrl":"https://doi.org/10.1215/21562261-2022-0020","url":null,"abstract":"Polyhedral products were defined by Bahri, Bendersky, Cohen and Gitler, to be spaces obtained as unions of certain product spaces indexed by the simplices of an abstract simplicial complex. In this paper we give a very general homotopy theoretic construction of polyhedral products over arbitrary pointed posets. We show that under certain restrictions on the poset $calp$, that include all known cases, the cohomology of the resulting spaces can be computed as an inverse limit over $calp$ of the cohomology of the building blocks. This motivates the definition of an analogous algebraic construction - the polyhedral tensor product. We show that for a large family of posets, the cohomology of the polyhedral product is given by the polyhedral tensor product. We then restrict attention to polyhedral posets, a family of posets that include face posets of simplicial complexes, and simplicial posets, as well as many others. We define the Stanley-Reisner ring of a polyhedral poset and show that, like in the classical cases, these rings occur as the cohomology of certain polyhedral products over the poset in question. For any pointed poset $calp$ we construct a simplicial poset $s(calp)$, and show that if $calp$ is a polyhedral poset then polyhedral products over $calp$ coincide up to homotopy with the corresponding polyhedral products over $s(calp)$.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46937007","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 : 2019-03-08DOI: 10.1215/21562261-2022-0010
Ben Salisbury, Travis Scrimshaw
It is shown that the direct limit of the semistandard decomposition tableau model for polynomial representations of the queer Lie superalgebra exists, which is believed to be the crystal for the upper half of the corresponding quantum group. An extension of this model to describe the direct limit combinatorially is given. Furthermore, it is shown that the polynomials representations may be recovered from the limit in most cases.
{"title":"Candidate for the crystal B(−∞) for the queer Lie superalgebra","authors":"Ben Salisbury, Travis Scrimshaw","doi":"10.1215/21562261-2022-0010","DOIUrl":"https://doi.org/10.1215/21562261-2022-0010","url":null,"abstract":"It is shown that the direct limit of the semistandard decomposition tableau model for polynomial representations of the queer Lie superalgebra exists, which is believed to be the crystal for the upper half of the corresponding quantum group. An extension of this model to describe the direct limit combinatorially is given. Furthermore, it is shown that the polynomials representations may be recovered from the limit in most cases.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47720720","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 : 2019-02-10DOI: 10.1215/21562261-10428494
T. Makino
The linearized operator for non-radial oscillations of spherically symmetric self-gravitating gaseous stars is analyzed in view of the functional analysis. The evolution of the star is supposed to be governed by the Euler-Poisson equations under the equation of state of the ideal gas, and the motion is supposed to be adiabatic. We consider the case of not necessarily isentropic, that is, not barotropic motions. Basic theory of self-adjoint realization of the linearized operator is established. Some problems in the investigation of the concrete properties of the spectrum of the linearized operator are proposed. The existence of eigenvalues which accumulate to 0 is proved in a mathematically rigorous fashion.The absence of continuous spectra and the completeness of eigenfunctions for the operators reduced by spherical harmonics is discussed.
{"title":"On linear adiabatic perturbations of spherically symmetric gaseous stars governed by the Euler–Poisson equations","authors":"T. Makino","doi":"10.1215/21562261-10428494","DOIUrl":"https://doi.org/10.1215/21562261-10428494","url":null,"abstract":"The linearized operator for non-radial oscillations of spherically symmetric self-gravitating gaseous stars is analyzed in view of the functional analysis. The evolution of the star is supposed to be governed by the Euler-Poisson equations under the equation of state of the ideal gas, and the motion is supposed to be adiabatic. We consider the case of not necessarily isentropic, that is, not barotropic motions. Basic theory of self-adjoint realization of the linearized operator is established. Some problems in the investigation of the concrete properties of the spectrum of the linearized operator are proposed. The existence of eigenvalues which accumulate to 0 is proved in a mathematically rigorous fashion.The absence of continuous spectra and the completeness of eigenfunctions for the operators reduced by spherical harmonics is discussed.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48259341","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 : 2019-01-04DOI: 10.1215/21562261-2021-0017
M. Handel, L. Mosher
Given a group acting on a Gromov hyperbolic space, Bestvina and Fujiwara introduced the WPD property --- weak proper discontinuity --- for studying the 2nd bounded cohomology of the group. We carry out a more general study of second bounded cohomology using a 'really' weak property discontinuity property known as WWPD that was introduced by Bestvina, Bromberg, and Fujiwara.
{"title":"Second bounded cohomology and WWPD","authors":"M. Handel, L. Mosher","doi":"10.1215/21562261-2021-0017","DOIUrl":"https://doi.org/10.1215/21562261-2021-0017","url":null,"abstract":"Given a group acting on a Gromov hyperbolic space, Bestvina and Fujiwara introduced the WPD property --- weak proper discontinuity --- for studying the 2nd bounded cohomology of the group. We carry out a more general study of second bounded cohomology using a 'really' weak property discontinuity property known as WWPD that was introduced by Bestvina, Bromberg, and Fujiwara.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45184575","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 : 2019-01-03DOI: 10.1215/21562261-2019-0002
B. Nica
We present two analytic applications of the fact that a hyperbolic group can be endowed with a strongly hyperbolic metric. The first application concerns the crossed-product C*-algebra defined by the action of a hyperbolic group on its boundary. We construct a natural time flow, involving the Busemann cocycle on the boundary. This flow has a natural KMS state, coming from the Hausdorff measure on the boundary, which is furthermore unique when the group is torsion-free. The second application is a short new proof of the fact that a hyperbolic group admits a proper isometric action on an $ell^p$-space, for large enough $p$.
{"title":"Two applications of strong hyperbolicity","authors":"B. Nica","doi":"10.1215/21562261-2019-0002","DOIUrl":"https://doi.org/10.1215/21562261-2019-0002","url":null,"abstract":"We present two analytic applications of the fact that a hyperbolic group can be endowed with a strongly hyperbolic metric. The first application concerns the crossed-product C*-algebra defined by the action of a hyperbolic group on its boundary. We construct a natural time flow, involving the Busemann cocycle on the boundary. This flow has a natural KMS state, coming from the Hausdorff measure on the boundary, which is furthermore unique when the group is torsion-free. The second application is a short new proof of the fact that a hyperbolic group admits a proper isometric action on an $ell^p$-space, for large enough $p$.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-2019-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42898363","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 : 2019-01-01DOI: 10.1215/21562261-2019-0013
F. Berger, F. Haslinger
We study necessary conditions for compactness of the weighted ∂-Neumann operator on the space L2(Cn, e−φ) for a plurisubharmonic function φ. Under the assumption that the corresponding weighted Bergman space of entire functions has infinite dimension, a weaker result is obtained by simpler methods. Moreover, we investigate (non-) compactness of the ∂-Neumann operator for decoupled weights, which are of the form φ(z) = φ1(z1) + · · ·+ φn(zn). More can be said if every ∆φj defines a nontrivial doubling measure.
{"title":"On some spectral properties of the weighted ∂¯-Neumann operator","authors":"F. Berger, F. Haslinger","doi":"10.1215/21562261-2019-0013","DOIUrl":"https://doi.org/10.1215/21562261-2019-0013","url":null,"abstract":"We study necessary conditions for compactness of the weighted ∂-Neumann operator on the space L2(Cn, e−φ) for a plurisubharmonic function φ. Under the assumption that the corresponding weighted Bergman space of entire functions has infinite dimension, a weaker result is obtained by simpler methods. Moreover, we investigate (non-) compactness of the ∂-Neumann operator for decoupled weights, which are of the form φ(z) = φ1(z1) + · · ·+ φn(zn). More can be said if every ∆φj defines a nontrivial doubling measure.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-2019-0013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66025736","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 : 2018-12-27DOI: 10.1215/21562261-2022-0009
Paolo Dolce
For an arithmetic surface $Xto B=operatorname{Spec} O_K$ the Deligne pairing $left<,,,right>colon operatorname{Pic}(X) times operatorname{Pic}(X) to operatorname{Pic}(B)$ gives the"schematic contribution"to the Arakelov intersection number. We present an idelic and adelic interpretation of the Deligne pairing; this is the first crucial step for a full idelic and adelic interpretation of the Arakelov intersection number. For the idelic approach we show that the Deligne pairing can be lifted to a pairing $left<,,,right>_i:ker(d^1_times)times ker(d^1_times)tooperatorname{Pic}(B) $, where $ker(d^1_times)$ is an important subspace of the two dimensional idelic group $mathbf A_X^times$. On the other hand, the argument for the adelic interpretation is entirely cohomological.
{"title":"Adelic geometry on arithmetic surfaces, I: Idelic and adelic interpretation of the Deligne pairing","authors":"Paolo Dolce","doi":"10.1215/21562261-2022-0009","DOIUrl":"https://doi.org/10.1215/21562261-2022-0009","url":null,"abstract":"For an arithmetic surface $Xto B=operatorname{Spec} O_K$ the Deligne pairing $left<,,,right>colon operatorname{Pic}(X) times operatorname{Pic}(X) to operatorname{Pic}(B)$ gives the\"schematic contribution\"to the Arakelov intersection number. We present an idelic and adelic interpretation of the Deligne pairing; this is the first crucial step for a full idelic and adelic interpretation of the Arakelov intersection number. For the idelic approach we show that the Deligne pairing can be lifted to a pairing $left<,,,right>_i:ker(d^1_times)times ker(d^1_times)tooperatorname{Pic}(B) $, where $ker(d^1_times)$ is an important subspace of the two dimensional idelic group $mathbf A_X^times$. On the other hand, the argument for the adelic interpretation is entirely cohomological.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44603646","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 : 2018-10-31DOI: 10.1215/21562261-2022-0007
Daniel Kasprowski
We give a short and elementary proof of the fact that every metric space of finite asymptotic dimension can be embedded into a finite product of trees.
我们给出了一个简短的初等证明，证明了每一个有限渐近维的度量空间都可以嵌入到树的有限积中。
{"title":"Coarse embeddings into products of trees","authors":"Daniel Kasprowski","doi":"10.1215/21562261-2022-0007","DOIUrl":"https://doi.org/10.1215/21562261-2022-0007","url":null,"abstract":"We give a short and elementary proof of the fact that every metric space of finite asymptotic dimension can be embedded into a finite product of trees.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48327717","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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