In this paper, the authors study the Cohen-Fischman-Westreich's double centralizer theorem for triangular Hopf algebras in the setting of almost-triangular Hopf algebras.
A linear mappingφfrom an algebra A into its bimodule M is called a centralizable mapping at G∈A ifφ(AB)=φ(A)B=Aφ(B)for each A and B in A with AB=G.In this paper,we prove that if M is a von Neumann algebra without...A linear mappingφfrom an algebra A into its bimodule M is called a centralizable mapping at G∈A ifφ(AB)=φ(A)B=Aφ(B)for each A and B in A with AB=G.In this paper,we prove that if M is a von Neumann algebra without direct summands of type I1 and type II,A is a*-subalgebra with M■A■LS(M)and G is a fixed element in A,then every continuous(with respect to the local measure topology t(M))centralizable mapping at G from A into M is a centralizer.展开更多
基于复Hilbert空间H上的一个完全分配可交换子空间格L,讨论L上的代数A lg L上的中心化映射。设Φ为A lg L上的一个可加映射,若对于任意的A,B∈A lg L,有2Φ(ABA)-(ABΦ(A)-Φ(A)BA)∈Z(A lg L),则存在A lg L的中心中的元素λ,使得对任意...基于复Hilbert空间H上的一个完全分配可交换子空间格L,讨论L上的代数A lg L上的中心化映射。设Φ为A lg L上的一个可加映射,若对于任意的A,B∈A lg L,有2Φ(ABA)-(ABΦ(A)-Φ(A)BA)∈Z(A lg L),则存在A lg L的中心中的元素λ,使得对任意的A∈A lg L,有Φ(A)=λA。展开更多
In this article, we revisit some aspects of the computation of the cohomology class of H2 (Witt, C)?using some methods in two-dimensional conformal field theory and conformal algebra to obtain the one-dimensional cent...In this article, we revisit some aspects of the computation of the cohomology class of H2 (Witt, C)?using some methods in two-dimensional conformal field theory and conformal algebra to obtain the one-dimensional central extension of the Witt algebra to the Virasoro algebra. Even though this is well-known in the context of standard mathematical physics literature, the operator product expansion of the energy-momentum tensor in two-dimensional conformal field theory is presented almost axiomatically. In this paper, we attempt to reformulate it with the help of a suitable modification of conformal algebra (as developed by V. Kac), and apply it to compute the representative element of the cohomology class which gives the desired central extension. This paper was written in the scope of an undergraduate’s exploration of conformal field theory and to gain insight on the subject from a mathematical perspective.展开更多
Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matri...Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given.As a particular case ,the matrix equation X-AXB=C over Ω is also considered.展开更多
Let g be a(twisted or untwisted)affine Kac-Moody algebra,and μ be a diagram automorphism of g.In this paper,we give an explicit realization for the universal central extensionˆg[μ]of the twisted loop algebra of g wi...Let g be a(twisted or untwisted)affine Kac-Moody algebra,and μ be a diagram automorphism of g.In this paper,we give an explicit realization for the universal central extensionˆg[μ]of the twisted loop algebra of g with respect toμ,which provides a Moody-Rao-Yokonuma presentation for the algebraˆg[μ]whenμis non-transitive,and the presentation is indeed related to the quantization of twisted toroidal Lie algebras.展开更多
In this paper, we study an infinite-dimensional Lie algebra Bq, called the q-analog Klein bottle Lie algebra. We show that Bq is a finitely generated simple Lie algebra with a unique (up to scalars) symmetric invari...In this paper, we study an infinite-dimensional Lie algebra Bq, called the q-analog Klein bottle Lie algebra. We show that Bq is a finitely generated simple Lie algebra with a unique (up to scalars) symmetric invariant bilinear form. The derivation algebra and the universal central extension of Bq are also determined.展开更多
This is the last in a series of three articles studying some quadratic algebras related to quantized matrix algebras. Here we determine the full set of so\|called cyclic representations of the quantized matrix algebra...This is the last in a series of three articles studying some quadratic algebras related to quantized matrix algebras. Here we determine the full set of so\|called cyclic representations of the quantized matrix algebra M\-q(3). These are irreducible representations in which all generators are invertible and the assumption on q is that it is a primitive m\|th root of 1, with m≥3.展开更多
设A lg L是Hilbert空间H上的一个CDC-代数,φ:A lg L®A lg L是一可加映射。证明了如果存在正整数mn1,满足对于任意的a?A lg L有φ(am+n+1)=amφ(a)an,那么存在A lg L的中心中的元素λ?Z(A lg L),使得对于任意的a?A lg L...设A lg L是Hilbert空间H上的一个CDC-代数,φ:A lg L®A lg L是一可加映射。证明了如果存在正整数mn1,满足对于任意的a?A lg L有φ(am+n+1)=amφ(a)an,那么存在A lg L的中心中的元素λ?Z(A lg L),使得对于任意的a?A lg L有φ(a)=λa。展开更多
Let Ω be a finite dimensional central algebra with an involutorial anti-automorphism and chartΩ≠2.Two systems of matrix equations over Ω are consid-ered.Necessary and sufficient conditions for the existences of ge...Let Ω be a finite dimensional central algebra with an involutorial anti-automorphism and chartΩ≠2.Two systems of matrix equations over Ω are consid-ered.Necessary and sufficient conditions for the existences of general solutions,andper(skew)selfconjugate solutions of the systems are given,respectively.展开更多
基金supported by the National Natural Science Foundation of China(No.11371088)the Natural Science Foundation of Jiangsu Province(No.BK2012736)
文摘In this paper, the authors study the Cohen-Fischman-Westreich's double centralizer theorem for triangular Hopf algebras in the setting of almost-triangular Hopf algebras.
基金supported by National Natural Science Foundation of China(Grant Nos.1180100511801342+6 种基金118010041187102111801050)supported by a Startup Fundation of Anhui Polytechnic University(Grant No.2017YQQ017)supported by Shaanxi Provincial Education Department(Grant No.19JK0130)supported by Research Foundation of Chongqing Educational Committee(Grant No.KJQN2018000538)We would like to thank the for their patience and useful comments.
文摘A linear mappingφfrom an algebra A into its bimodule M is called a centralizable mapping at G∈A ifφ(AB)=φ(A)B=Aφ(B)for each A and B in A with AB=G.In this paper,we prove that if M is a von Neumann algebra without direct summands of type I1 and type II,A is a*-subalgebra with M■A■LS(M)and G is a fixed element in A,then every continuous(with respect to the local measure topology t(M))centralizable mapping at G from A into M is a centralizer.
文摘基于复Hilbert空间H上的一个完全分配可交换子空间格L,讨论L上的代数A lg L上的中心化映射。设Φ为A lg L上的一个可加映射,若对于任意的A,B∈A lg L,有2Φ(ABA)-(ABΦ(A)-Φ(A)BA)∈Z(A lg L),则存在A lg L的中心中的元素λ,使得对任意的A∈A lg L,有Φ(A)=λA。
文摘In this article, we revisit some aspects of the computation of the cohomology class of H2 (Witt, C)?using some methods in two-dimensional conformal field theory and conformal algebra to obtain the one-dimensional central extension of the Witt algebra to the Virasoro algebra. Even though this is well-known in the context of standard mathematical physics literature, the operator product expansion of the energy-momentum tensor in two-dimensional conformal field theory is presented almost axiomatically. In this paper, we attempt to reformulate it with the help of a suitable modification of conformal algebra (as developed by V. Kac), and apply it to compute the representative element of the cohomology class which gives the desired central extension. This paper was written in the scope of an undergraduate’s exploration of conformal field theory and to gain insight on the subject from a mathematical perspective.
基金Supported by the Natural Science Foundation of China(10071078)Supported by the Natural Science Foundation of Shandong Province(Q99A08)
文摘Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given.As a particular case ,the matrix equation X-AXB=C over Ω is also considered.
基金supported by National Natural Science Foundation of China(Grant Nos.11531004 and 11701183)the Fundamental Research Funds for the Central Universities(Grant No.20720190069)the Simons Foundation(Grant No.198129)。
文摘Let g be a(twisted or untwisted)affine Kac-Moody algebra,and μ be a diagram automorphism of g.In this paper,we give an explicit realization for the universal central extensionˆg[μ]of the twisted loop algebra of g with respect toμ,which provides a Moody-Rao-Yokonuma presentation for the algebraˆg[μ]whenμis non-transitive,and the presentation is indeed related to the quantization of twisted toroidal Lie algebras.
基金The first author was supported in part by the NSFC (10931006, 10871125) and the Innovation Program of Shanghai Municipal Education Commission (11ZZ18). The second author was supported by the NSFC (11326060). The third author was supported in part by the NSFC (11101285, 11026042, 11071068), the Shanghai Natural Science Foundation (11ZR1425900), the Innovation Program of Shanghai Municipal Education Commission (11YZ85), the Academic Discipline Project of Shanghai Normal University (DZL803) and ZJNSF (Y6100148).
文摘In this paper, we study an infinite-dimensional Lie algebra Bq, called the q-analog Klein bottle Lie algebra. We show that Bq is a finitely generated simple Lie algebra with a unique (up to scalars) symmetric invariant bilinear form. The derivation algebra and the universal central extension of Bq are also determined.
基金Supported by the National Natural Science Foundationof China(No.194 0 10 2 1)
文摘This is the last in a series of three articles studying some quadratic algebras related to quantized matrix algebras. Here we determine the full set of so\|called cyclic representations of the quantized matrix algebra M\-q(3). These are irreducible representations in which all generators are invertible and the assumption on q is that it is a primitive m\|th root of 1, with m≥3.
文摘设A lg L是Hilbert空间H上的一个CDC-代数,φ:A lg L®A lg L是一可加映射。证明了如果存在正整数mn1,满足对于任意的a?A lg L有φ(am+n+1)=amφ(a)an,那么存在A lg L的中心中的元素λ?Z(A lg L),使得对于任意的a?A lg L有φ(a)=λa。
基金Foundation item:Supported by the National Natural Science Foundation of China(10071078)Natural Science Foundation of Shandong Province(Q99A08)
文摘Let Ω be a finite dimensional central algebra with an involutorial anti-automorphism and chartΩ≠2.Two systems of matrix equations over Ω are consid-ered.Necessary and sufficient conditions for the existences of general solutions,andper(skew)selfconjugate solutions of the systems are given,respectively.