In this paper, it is proved that the global dimension of a Yetter-Drinfel’d Hopf algebra coincides with the projective dimension of its trivial module k.
The concept of （f, σ）-pair （B, H）is introduced, where B and H are Hopf algebras. A braided tensor category which is a tensor subcategory of the category ^HM of left H-comodules through an （f, σ）-pair is constr...The concept of （f, σ）-pair （B, H）is introduced, where B and H are Hopf algebras. A braided tensor category which is a tensor subcategory of the category ^HM of left H-comodules through an （f, σ）-pair is constructed. In particularly, a Yang-Baxter equation is got. A Hopf algebra is constructed as well in the Yetter-Drinfel＇d category H^HYD by twisting the multiplication of B.展开更多
It is known that any strict tensor category （C, I） can determine a strict braided tensor category Z （ C）, the centre of C. When A is a finite Hopf algebra, Drinfel’d has proved that Z（<sub>A</sub>M）...It is known that any strict tensor category （C, I） can determine a strict braided tensor category Z （ C）, the centre of C. When A is a finite Hopf algebra, Drinfel’d has proved that Z（<sub>A</sub>M） is equivalent to <sub>D（A）</sub>M as a braided tensor category, where <sub>A</sub>M is the left A-module category, and D （A） is the Drinfel’d double of A. This is the categorical interpretation of D （A）.Z（<sub>4</sub>M） is proved to be equivalent to the Yetter-Drinfel’ d module category <sub>A</sub>Y D<sup>4</sup> as a braided tensor category for any Hopf algebra A. Furthermore, for right A-comodule category M<sup>A</sup> , Z（M<sup>A</sup>） is proved to be equivalent to the Yetter-Drinfel’ d module category <sub>A</sub>Y D<sup>4</sup> as a braided tensor category. But, in the two cases, the Yetter-Drinfel’ d module category <sub>A</sub>Y D<sup>A</sup> has different braided tensor structures.展开更多
This paper introduces the concept of’ symmetric centres’ of braided monoidal categories. Let H be a Hopf algebra with bijective antipode over a field k. We address the symmetric centre of the Yetter-Drinfel’d mod黮...This paper introduces the concept of’ symmetric centres’ of braided monoidal categories. Let H be a Hopf algebra with bijective antipode over a field k. We address the symmetric centre of the Yetter-Drinfel’d mod黮e category and show that a left Yetter-Drinfel’d mod黮e M belongs to the symmetric centre of if and only if M is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give a sufficient and necessary condition for the braid of to induce the braid of or equivalently, the braid of , where A is a quantum commutative H-module algebra.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10726039)the Leading Academic Discipline Program and 211 Project for Shanghai University of Finance and Economics (the 3rd phase)
文摘In this paper, it is proved that the global dimension of a Yetter-Drinfel’d Hopf algebra coincides with the projective dimension of its trivial module k.
基金Supported by the Zhejiang Provincial Natural Science Foundation (Y607075)
文摘The concept of （f, σ）-pair （B, H）is introduced, where B and H are Hopf algebras. A braided tensor category which is a tensor subcategory of the category ^HM of left H-comodules through an （f, σ）-pair is constructed. In particularly, a Yang-Baxter equation is got. A Hopf algebra is constructed as well in the Yetter-Drinfel＇d category H^HYD by twisting the multiplication of B.
文摘It is known that any strict tensor category （C, I） can determine a strict braided tensor category Z （ C）, the centre of C. When A is a finite Hopf algebra, Drinfel’d has proved that Z（<sub>A</sub>M） is equivalent to <sub>D（A）</sub>M as a braided tensor category, where <sub>A</sub>M is the left A-module category, and D （A） is the Drinfel’d double of A. This is the categorical interpretation of D （A）.Z（<sub>4</sub>M） is proved to be equivalent to the Yetter-Drinfel’ d module category <sub>A</sub>Y D<sup>4</sup> as a braided tensor category for any Hopf algebra A. Furthermore, for right A-comodule category M<sup>A</sup> , Z（M<sup>A</sup>） is proved to be equivalent to the Yetter-Drinfel’ d module category <sub>A</sub>Y D<sup>4</sup> as a braided tensor category. But, in the two cases, the Yetter-Drinfel’ d module category <sub>A</sub>Y D<sup>A</sup> has different braided tensor structures.
文摘This paper introduces the concept of’ symmetric centres’ of braided monoidal categories. Let H be a Hopf algebra with bijective antipode over a field k. We address the symmetric centre of the Yetter-Drinfel’d mod黮e category and show that a left Yetter-Drinfel’d mod黮e M belongs to the symmetric centre of if and only if M is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give a sufficient and necessary condition for the braid of to induce the braid of or equivalently, the braid of , where A is a quantum commutative H-module algebra.
