The notions of quasi k-Gorenstein algebras and W^t-approximation representations are introduced. The existence and uniqueness (up to projective equivalences) of W^t-approximation representations over quasi k-Gorenstei...The notions of quasi k-Gorenstein algebras and W^t-approximation representations are introduced. The existence and uniqueness (up to projective equivalences) of W^t-approximation representations over quasi k-Gorenstein algebras are established. Some applications of W^t-approximation representations to homologically finite subcategories are given.展开更多
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#σH are coincident. This is...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#σH 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#σH. Then, using this result, it is proven that A is a finite dimensional CM-finite Gorenstein algebra if and only if so is A#σH.展开更多
We prove that for a Frobenius extension,a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective.For a separable Frobenius extension be...We prove that for a Frobenius extension,a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective.For a separable Frobenius extension between Artin algebras,we obtain that the extension algebra is CM(Cohen-Macaulay)-finite(resp.CM-free)if and only if so is the base algebra.Furthermore,we prove that the representation dimension of Artin algebras is invariant under separable Frobenius extensions.展开更多
文摘The notions of quasi k-Gorenstein algebras and W^t-approximation representations are introduced. The existence and uniqueness (up to projective equivalences) of W^t-approximation representations over quasi k-Gorenstein algebras are established. Some applications of W^t-approximation representations to homologically finite subcategories are given.
基金supported by National Natural Science Foundation of China (Grant No.11171296)the Zhejiang Provincial Natural Science Foundation of China (Grant No. D7080064)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110101110010)
文摘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#σH 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#σH. Then, using this result, it is proven that A is a finite dimensional CM-finite Gorenstein algebra if and only if so is A#σH.
基金supported by National Natural Science Foundation of China(Grant No.11571329)the Natural Science Foundation of Anhui Province(Grant No.1708085MA01)
文摘We prove that for a Frobenius extension,a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective.For a separable Frobenius extension between Artin algebras,we obtain that the extension algebra is CM(Cohen-Macaulay)-finite(resp.CM-free)if and only if so is the base algebra.Furthermore,we prove that the representation dimension of Artin algebras is invariant under separable Frobenius extensions.
