We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules.This is motivated by the Nakayama conjecture and an approach of MartinezVilla to the Auslan...We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules.This is motivated by the Nakayama conjecture and an approach of MartinezVilla to the Auslander-Reiten conjecture on stable equivalences.We show that the Frobenius parts of Frobenius extensions are again Frobenius extensions.Furthermore,let A and B be finite-dimensional algebras over a field k,and let domdim(_AX)stand for the dominant dimension of an A-module X.If_BM_A is a Frobenius bimodule,then domdim(A)domdim(_BM)and domdim(B)domdim(_AHom_B(M,B)).In particular,if B■A is a left-split(or right-split)Frobenius extension,then domdim(A)=domdim(B).These results are applied to calculate flat-dominant dimensions of a number of algebras:shew group algebras,stably equivalent algebras,trivial extensions and Markov extensions.We also prove that the universal(quantised)enveloping algebras of semisimple Lie algebras are QF-3 rings in the sense of Morita.展开更多
Let V be a vertex operator superalgebra and m,n ∈ 21Z+. We construct an An(V ) -Am(V )-bimodule An,m(V ) which characterizes the action of V from the level m subspace to level n subspace of an admissible V -module. W...Let V be a vertex operator superalgebra and m,n ∈ 21Z+. We construct an An(V ) -Am(V )-bimodule An,m(V ) which characterizes the action of V from the level m subspace to level n subspace of an admissible V -module. We also construct the Verma type admissible V -module from an Am(V )-module by using展开更多
Tilting pair was introduced by Miyashita in 2001 as a generalization of tilting module. In this paper, we construct a tilting left Endh(C)-right Endh(T)-bimodule for a given tilting pairs (C,T) in modh, where A ...Tilting pair was introduced by Miyashita in 2001 as a generalization of tilting module. In this paper, we construct a tilting left Endh(C)-right Endh(T)-bimodule for a given tilting pairs (C,T) in modh, where A is an Artin algebra.展开更多
The theory of L-R smash product is extended to multiplier Hopf algebras and a sufficient condition for L-R smash product to be regular multiplier Hopf algebras is given. In particular, the result of the paper implies ...The theory of L-R smash product is extended to multiplier Hopf algebras and a sufficient condition for L-R smash product to be regular multiplier Hopf algebras is given. In particular, the result of the paper implies Delvaux's main theorem in the case of smash products.展开更多
The main aim of this paper is to study the twisting theory of weak Hopf algebras and give an equivalence between the (braided) monoidal categories of weak Hopf bimodules over the original and the twisted weak Hopf a...The main aim of this paper is to study the twisting theory of weak Hopf algebras and give an equivalence between the (braided) monoidal categories of weak Hopf bimodules over the original and the twisted weak Hopf algebra to generalize the result from Oeckl (2000).展开更多
L-octo-algebra with 8 operations as the Lie algebraic analogue of octo- algebra such that the sum of 8 operations is a Lie algebra is discussed. Any octo- algebra is an L-octo-algebra. The relationships among L-octo-a...L-octo-algebra with 8 operations as the Lie algebraic analogue of octo- algebra such that the sum of 8 operations is a Lie algebra is discussed. Any octo- algebra is an L-octo-algebra. The relationships among L-octo-algebras, L-quadri- algebras, L-dendriform algebras, pre-Lie algebras and Lie algebras are given. The close relationships between L-octo-algebras and some interesting structures like Rota- Baxter operators, classical Yang-Baxter equations and some bilinear forms satisfying certain conditions are given also.展开更多
Given an r discrete, principal and amenable groupoid, the bijective correspondence between the family of the closed C 0(G 0) bimodules of C *(G) and the family of the open subsets of the groupoid G is established. Mor...Given an r discrete, principal and amenable groupoid, the bijective correspondence between the family of the closed C 0(G 0) bimodules of C *(G) and the family of the open subsets of the groupoid G is established. Moreover they are rigidity.展开更多
Let (K, M,H) be an upper triangular bimodule problem. Briistle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K., M, H) is quasi-hered...Let (K, M,H) be an upper triangular bimodule problem. Briistle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K., M, H) is quasi-hereditary, and there is an equivalence between the category of△-good modules of A and Mat(K, M). In this note, based on the tame theorem for bimodule problems, we show that if the algebra A associated with an upper triangular bimodule problem is of△-tame representation type, then the category F(△) has the homogeneous property, i.e. almost all modules in F(△) are isomorphic to their Auslander-Reiten translations. Moreover, if (K, M,H)is an upper triangular bipartite bimodule problem, then A is of△-tame representation type if and only if F(△) is homogeneous.展开更多
Two theorems are established which properly extend the class of artinian rings with Morita duality. A question of Anh about QF rings is answered in the negative.
As the dual of the Auslander transpose and the resulting k-torsionfree module,the cotranspose and k-cotorsionfree module with respect to a semidualizing bimodule have been introduced recently.In this paper we first in...As the dual of the Auslander transpose and the resulting k-torsionfree module,the cotranspose and k-cotorsionfree module with respect to a semidualizing bimodule have been introduced recently.In this paper we first investigate the relation between relative k-cotorsionfree modules and relative k-cosyzygy modules.Then we study the extension closure of these two classes of modules.展开更多
Extending the notion of property T of finite von Neumann algebras to general yon Neu- mann algebras, we define and study in this paper property T** for (possibly non-unital) C*-algebras. We obtain several results...Extending the notion of property T of finite von Neumann algebras to general yon Neu- mann algebras, we define and study in this paper property T** for (possibly non-unital) C*-algebras. We obtain several results of property T** parallel to those of property T for unital C*-algebras. Moreover, we show that a discrete group F has property T if and only if the group C*-algebra C*(F) (or equivalently, the reduced group C*-algebra C*(F)) has property T**. We also show that the compact operators K(g2) has property T** but co does not have property T**.展开更多
基金supported by the Beijing Natural Science Foundation(Grant No.1192004)National Natural Science Foundation of China(Grant No.11331006)。
文摘We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules.This is motivated by the Nakayama conjecture and an approach of MartinezVilla to the Auslander-Reiten conjecture on stable equivalences.We show that the Frobenius parts of Frobenius extensions are again Frobenius extensions.Furthermore,let A and B be finite-dimensional algebras over a field k,and let domdim(_AX)stand for the dominant dimension of an A-module X.If_BM_A is a Frobenius bimodule,then domdim(A)domdim(_BM)and domdim(B)domdim(_AHom_B(M,B)).In particular,if B■A is a left-split(or right-split)Frobenius extension,then domdim(A)=domdim(B).These results are applied to calculate flat-dominant dimensions of a number of algebras:shew group algebras,stably equivalent algebras,trivial extensions and Markov extensions.We also prove that the universal(quantised)enveloping algebras of semisimple Lie algebras are QF-3 rings in the sense of Morita.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10571119, 10671027)
文摘Let V be a vertex operator superalgebra and m,n ∈ 21Z+. We construct an An(V ) -Am(V )-bimodule An,m(V ) which characterizes the action of V from the level m subspace to level n subspace of an admissible V -module. We also construct the Verma type admissible V -module from an Am(V )-module by using
基金Supported by the National Natural Science Foundation of China (Grant Nos.1097102410826036)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.200802860024)the Natural Science Foundation of Jiangsu Province (Grant No.BK2010393)the Scientific Research Foundation of Guangxi University (Grant No.XJZ100246)
文摘Tilting pair was introduced by Miyashita in 2001 as a generalization of tilting module. In this paper, we construct a tilting left Endh(C)-right Endh(T)-bimodule for a given tilting pairs (C,T) in modh, where A is an Artin algebra.
基金Supported by the Ningbo Natural Science Foundation(2006A610089)
文摘The theory of L-R smash product is extended to multiplier Hopf algebras and a sufficient condition for L-R smash product to be regular multiplier Hopf algebras is given. In particular, the result of the paper implies Delvaux's main theorem in the case of smash products.
基金Partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education(20060286006)the National Natural Science Foundation of China(10571026)the Southeast University Fund(XJ0707273).
文摘The main aim of this paper is to study the twisting theory of weak Hopf algebras and give an equivalence between the (braided) monoidal categories of weak Hopf bimodules over the original and the twisted weak Hopf algebra to generalize the result from Oeckl (2000).
文摘L-octo-algebra with 8 operations as the Lie algebraic analogue of octo- algebra such that the sum of 8 operations is a Lie algebra is discussed. Any octo- algebra is an L-octo-algebra. The relationships among L-octo-algebras, L-quadri- algebras, L-dendriform algebras, pre-Lie algebras and Lie algebras are given. The close relationships between L-octo-algebras and some interesting structures like Rota- Baxter operators, classical Yang-Baxter equations and some bilinear forms satisfying certain conditions are given also.
文摘Given an r discrete, principal and amenable groupoid, the bijective correspondence between the family of the closed C 0(G 0) bimodules of C *(G) and the family of the open subsets of the groupoid G is established. Moreover they are rigidity.
基金This work was partially supported by the National Natural Science Foundation of China (Grant Nos.10201007 and A0324614)the Natural Science Foundation of Shandong Province (Grant No.Y2006A03)
文摘We show that every local 3-cocycle of a von Neumann algebra R into an arbitrary unital dual R-bimodule S is a 3-cocycle.
基金This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10426014,10501010 and 19331030)the Foundation of Hubei Provincial Department of Education (Grant No.D200510005).
文摘Let (K, M,H) be an upper triangular bimodule problem. Briistle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K., M, H) is quasi-hereditary, and there is an equivalence between the category of△-good modules of A and Mat(K, M). In this note, based on the tame theorem for bimodule problems, we show that if the algebra A associated with an upper triangular bimodule problem is of△-tame representation type, then the category F(△) has the homogeneous property, i.e. almost all modules in F(△) are isomorphic to their Auslander-Reiten translations. Moreover, if (K, M,H)is an upper triangular bipartite bimodule problem, then A is of△-tame representation type if and only if F(△) is homogeneous.
文摘Two theorems are established which properly extend the class of artinian rings with Morita duality. A question of Anh about QF rings is answered in the negative.
基金This research was partially supported by NSFC(11401147,11531002)Natural Science Foundation of Shandong Province of China(ZR2017BA028).
文摘As the dual of the Auslander transpose and the resulting k-torsionfree module,the cotranspose and k-cotorsionfree module with respect to a semidualizing bimodule have been introduced recently.In this paper we first investigate the relation between relative k-cotorsionfree modules and relative k-cosyzygy modules.Then we study the extension closure of these two classes of modules.
文摘Extending the notion of property T of finite von Neumann algebras to general yon Neu- mann algebras, we define and study in this paper property T** for (possibly non-unital) C*-algebras. We obtain several results of property T** parallel to those of property T for unital C*-algebras. Moreover, we show that a discrete group F has property T if and only if the group C*-algebra C*(F) (or equivalently, the reduced group C*-algebra C*(F)) has property T**. We also show that the compact operators K(g2) has property T** but co does not have property T**.