通过分析半单Hopf代数类群元所构成群的阶数,得到了特征为零代数闭域上pq3维半单Hopf代数的结构:它们或者是半可解的,或者同构于Radford双积R#A,其中:p,q是满足条件p>q2的素数;A是q3维半单Hopf代数;R是Yetter-Drinfeld模范畴A A Y D...通过分析半单Hopf代数类群元所构成群的阶数,得到了特征为零代数闭域上pq3维半单Hopf代数的结构:它们或者是半可解的,或者同构于Radford双积R#A,其中:p,q是满足条件p>q2的素数;A是q3维半单Hopf代数;R是Yetter-Drinfeld模范畴A A Y D中的p维半单Hopf代数.展开更多
Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD（H） is considered, where YD （H） means the disjoint union of the c...Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD（H） is considered, where YD （H） means the disjoint union of the category of generalized Yetter-Drinfeld modules nYD^H（ α, β） for any α, β E Aut Hopf（H）. First, the fact that YD（H） is closed under Mor is proved. Secondly, based on the properties of finitely generated projective modules and semisimplicity of H, YD（H） satisfies the exact condition. Thus each object in YD（H） can be decomposed into simple ones since H is noetherian and cosemisimple. Finally, it is proved that YD （H） is a sernisimple category.展开更多
Let H be a finite-dimensional Hopf algebra and assume that both H and H＊ are semisimple. The main result of this paper is to show that the representation dimension is an invariant under cleft extensions of H, that is...Let H be a finite-dimensional Hopf algebra and assume that both H and H＊ are semisimple. The main result of this paper is to show that the representation dimension is an invariant under cleft extensions of H, that is, rep.dim（A） = rep.dim（A^CaH）. Some of the applications of this equality are also given.展开更多
Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a l-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full m...Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a l-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full matrix algebra over some right coideal subalgebra N of H. The correspondence between A and such N, and the special case A = k（X） of function algebra on a finite set X are considered.展开更多
文摘通过分析半单Hopf代数类群元所构成群的阶数,得到了特征为零代数闭域上pq3维半单Hopf代数的结构:它们或者是半可解的,或者同构于Radford双积R#A,其中:p,q是满足条件p>q2的素数;A是q3维半单Hopf代数;R是Yetter-Drinfeld模范畴A A Y D中的p维半单Hopf代数.
基金supported by the NSFC(11201231)the China Postdoctoral Science Foundation(2012M511643)+1 种基金the Jiangsu Planned Projects for Postdoctoral Research Funds(1102041C)Agricultural Machinery Bureau Foundation of Jiangsu Province(GXZ11003)
基金supported by NSF of China(10771183、11201231)Docurate Foundation of Ministry of Education of China(200811170001)Jiangsu Planned Projects for Postdoctoral Research Funds(1102041C)~~
基金The National Natural Science Foundation of China(No.11371088)the Fundamental Research Funds for the Central Universities(No.3207013906)the Natural Science Foundation of Jiangsu Province(No.BK2012736)
文摘Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD（H） is considered, where YD （H） means the disjoint union of the category of generalized Yetter-Drinfeld modules nYD^H（ α, β） for any α, β E Aut Hopf（H）. First, the fact that YD（H） is closed under Mor is proved. Secondly, based on the properties of finitely generated projective modules and semisimplicity of H, YD（H） satisfies the exact condition. Thus each object in YD（H） can be decomposed into simple ones since H is noetherian and cosemisimple. Finally, it is proved that YD （H） is a sernisimple category.
基金partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100091110034)National Natural Science Foundation of China(Grant Nos. 10771095, 10801069)the Natural Science Foundation of Jiangsu Province of China (Grant No.BK2010047)
文摘Let H be a finite-dimensional Hopf algebra and assume that both H and H＊ are semisimple. The main result of this paper is to show that the representation dimension is an invariant under cleft extensions of H, that is, rep.dim（A） = rep.dim（A^CaH）. Some of the applications of this equality are also given.
基金supported by the National Natural Science Foundation of China(No.10731070)
文摘Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a l-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full matrix algebra over some right coideal subalgebra N of H. The correspondence between A and such N, and the special case A = k（X） of function algebra on a finite set X are considered.
