The global dimensions of crossed products and crossed coproducts |
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Authors: | Teng Xia Ju |
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Institution: | (1) Department of Mathematics, Nanjing University, Nanjing, 210093, P. R. China;(2) Faculty of Science, Nantong University, Nantong, 226007, P. R. China |
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Abstract: | In this paper, we show that if H is a finite-dimensional Hopf algebra such that H and H* are semisimple, then gl.dim(A#
σ
H)=gl.dim(A), where σ is a convolution invertible cocycle. We also discuss the relationship of global dimensions between the crossed product A#
σ
H and the algebra A, where A is coacted by H. Dually, we give a sufficient condition for a finite dimensional coalgebra C and a finite dimensional semisimple Hopf algebra H such that gl.dim(C ⋊
α
H)=gl.dim(C).
Supported by the National Natural Science Foundation of China (Grant No. 10771182) and Nantong University Foundation (Grant
No. xj06Z009) |
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Keywords: | global dimension crossed products crossed coproducts twistings |
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