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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.12 P.2088-2092


Global dimension of weak smash product

Author(s):  JIA Ling, LI Fang

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   jialing471@126.com

Key Words:  Weak Hopf algebra, Weak smash product, Gobal dimension

JIA Ling, LI Fang. Global dimension of weak smash product[J]. Journal of Zhejiang University Science A, 2006, 7(12): 2088-2092.

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In Artin algebra representation theory there is an important result which states that when the order of G is invertible in Λ then gl.dim(ΛG)=gl.dim(Λ). With the development of Hopf algebra theory, this result is generalized to smash product algebra. As known, weak Hopf algebra is an important generalization of Hopf algebra. In this paper we give the more general result, that is the relation of homological dimension between an algebra A and weak smash product algebra A#H, where H is a finite dimensional weak Hopf algebra over a field k and A is an H-module algebra.

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[9] Zhu, J.G., 2005. Cosemisimple coextesnsion and homological dimension of smash coproduct. Acta Mathematica Sinica, English Series, 21(3):563-568.

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