Categorical methods in Hopf algebras


  • Wang Dingguo
  • Yang Shilin
  • Ji Qingzhong



In this paper, we first study the adjoint relationship of general functors between two Grothendieck categories. Then apply those results to obtain information about the connections of the categories $ A \# H $-mod and $ A^H $-mod, resp. $ {\cal M}^{C \rtimes H} $ and $ {\cal M}^{C^{coH}} $, where $ A $ is an $ H $-module algebra and $ C $ is an $ H $-comodule coalgebra. In particular, the relationships between the (co)generators, injectivity and projectivity of $ A \# H $-modules and the corresponding property of $ A^H $-modules are given, the relationships between the injective dimension $ A_A $ the corresponding dimension of $ A_{A^H}^H $ and $ A \# H_{A \# H} $ are also established.

Author Biographies

Wang Dingguo

Department of Mathematics, Qufu Normal University, Qufu, Shandong 273165, P. R. China.

Yang Shilin

Department of Applied Mathematics, Beijing Polytechnic University, Beijing 100022, P. R. China.

Ji Qingzhong

Department of Applied Mathematics, Qingdao Ocean University, Qingdao, Shandong 266070, P. R. China.



How to Cite

Dingguo, W., Shilin, Y., & Qingzhong, J. (2001). Categorical methods in Hopf algebras. Tamkang Journal of Mathematics, 32(4), 281–292.