This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras.
The Yetter-Drinfeld category of the Hopf algebra over a field is a prebraided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in ...The Yetter-Drinfeld category of the Hopf algebra over a field is a prebraided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in the weak Hopf algebra over a field k. For a weak Hopf algebra A in left Yetter-Drinfeld category HHYD, we prove that the weak biproducts of A and H is a weak Hopf algebra.展开更多
We give the Fundamental Theorem for Hopf modules in the category of Yetter-Drinfeld modules , where L is a quasitriangular weak Hopf algebra with a bijective antipode. We also show that H* has a right H-Hopf mod...We give the Fundamental Theorem for Hopf modules in the category of Yetter-Drinfeld modules , where L is a quasitriangular weak Hopf algebra with a bijective antipode. We also show that H* has a right H-Hopf module structure in the Yetter-Drinfeld category. As an application we deduce the existence and uniqueness of right integral from it.展开更多
Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d（y）, which is a weak Hopf algebra. We also study t...Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d（y）, which is a weak Hopf algebra. We also study the highest weight module over the weak quantum algebra wUdq^d（y） and weak A-forms of wUq^d（y）.展开更多
In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. A...In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. Also, from these results, we deduce a version of Maschke＇s Theorem for （H, B）-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B.展开更多
In this paper, the fundamental theorem of Yetter-Drinfeld Hopf module is proved. As applications, the freedom of tensor and twisted tensor of two Yetter-Drinfeld Hopf algebras is given. Let A be a Yetter-Drinfeld Hopf...In this paper, the fundamental theorem of Yetter-Drinfeld Hopf module is proved. As applications, the freedom of tensor and twisted tensor of two Yetter-Drinfeld Hopf algebras is given. Let A be a Yetter-Drinfeld Hopf algebra. It is proved that the category of A-bimodule is equivalent to the category of ? -twisted module.展开更多
In this paper, we introduce several centralizer constructions in a monoidal context and establish a monoidal equivalence with the category of Yetter-Drinfeld modules over a weak braided Hopf monoid. We apply the gener...In this paper, we introduce several centralizer constructions in a monoidal context and establish a monoidal equivalence with the category of Yetter-Drinfeld modules over a weak braided Hopf monoid. We apply the general result to the calculus of the center in module categories.展开更多
基金the National Natural Science Foundation of China(10301033 and 10271113)
文摘This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras.
基金The NSF (200510476001) of Education Department of Henan Province.
文摘The Yetter-Drinfeld category of the Hopf algebra over a field is a prebraided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in the weak Hopf algebra over a field k. For a weak Hopf algebra A in left Yetter-Drinfeld category HHYD, we prove that the weak biproducts of A and H is a weak Hopf algebra.
文摘We give the Fundamental Theorem for Hopf modules in the category of Yetter-Drinfeld modules , where L is a quasitriangular weak Hopf algebra with a bijective antipode. We also show that H* has a right H-Hopf module structure in the Yetter-Drinfeld category. As an application we deduce the existence and uniqueness of right integral from it.
基金Supported in part by the Scientific Research Foundation of Zhejiang Provincial Education Department under grant number 20040322It is also sponsored by SRF for ROCS,SEM
文摘Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d（y）, which is a weak Hopf algebra. We also study the highest weight module over the weak quantum algebra wUdq^d（y） and weak A-forms of wUq^d（y）.
基金Ministerio de Educacidn y Ciencia Projects MTM2006-14908-C02-01,MTM2007-62427FEDER
文摘In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. Also, from these results, we deduce a version of Maschke＇s Theorem for （H, B）-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B.
文摘In this paper, the fundamental theorem of Yetter-Drinfeld Hopf module is proved. As applications, the freedom of tensor and twisted tensor of two Yetter-Drinfeld Hopf algebras is given. Let A be a Yetter-Drinfeld Hopf algebra. It is proved that the category of A-bimodule is equivalent to the category of ? -twisted module.
基金Supported by Educational Ministry Key Foundation of China(108154)Na- tional Natural Science Foundation of China(10871170)Young Teachers of College of Science,Nanjing Agricultural University(LXY20090101)
基金the Educational Ministry Science Technique Research Key Foundation of China(108154)the College Special Research Doctoral Disciplines point Fund(2010097110040)+2 种基金the National Natural Science Foundation of China(10871170)the National Natural Science Foundation of Guangxi(2011GXNSFA018144)the Fundamental Research Funds for the Central Universities(KYZ201125)
基金Supported by Ministerio de Ciencia e Innovación,project MTM2010-15634Supported by FEDER
文摘In this paper, we introduce several centralizer constructions in a monoidal context and establish a monoidal equivalence with the category of Yetter-Drinfeld modules over a weak braided Hopf monoid. We apply the general result to the calculus of the center in module categories.
