Derived representation type and Gorenstein projective modules of an algebra under crossed product

作者：Li Fang; Sun LongGang^*

来源：Science China Mathematics, 2013, 56(3): 531-540.

DOI：10.1007/s11425-012-4469-9

• finite Cohen-Macaulay type
• crossed product
• derived representation type
• Gorenstein projective module

Let H and its dual H* be finite dimensional semisimple Hopf algebras. In this paper, we firstly prove that the derived representation types of an algebra A and the crossed product algebra A# H-sigma are coincident. This is an improvement of the conclusion about representation type of an algebra in Li and Zhang [Sci China Ser A, 2006, 50: 1-13]. Secondly, we give the relationship between Gorenstein projective modules over A and that over A# H-sigma. Then, using this result, it is proven that A is a finite dimensional CM-finite Gorenstein algebra if and only if so is A# H-sigma.

• 出版日期2013-3
• 单位浙江大学