Let A and B be Artin R-algebras of finite Cohen-Macaulay type. Then we prove that, if A and B are standard derived equivalent, then their Cohen-Macaulay Auslander algebras are also derived equivalent. And we show that...Let A and B be Artin R-algebras of finite Cohen-Macaulay type. Then we prove that, if A and B are standard derived equivalent, then their Cohen-Macaulay Auslander algebras are also derived equivalent. And we show that Gorenstein projective conjecture is an invariant under standard derived equivalence between Artin R-algebras.展开更多
In this article we investigate the relations between the Gorenstein projective dimensions of Λ-modules and their socles for re-minimal Auslander-Gorenstein algebras Λ.First we give a description of projective-inject...In this article we investigate the relations between the Gorenstein projective dimensions of Λ-modules and their socles for re-minimal Auslander-Gorenstein algebras Λ.First we give a description of projective-injective Λ-modules in terms of their socles.Then we prove that a Λ-module N has Gorenstein projective dimension at most n if and only if its socle has Gorenstein projective dimension at most n if and only if N is cogenerated by a projective Λ-module.Furthermore,we show that n-minimal Auslander-Gorenstein algebras can be characterised by the relations between the Gorenstein projective dimensions of modules and their socles.展开更多
We build a connection between iterated tilted algebras with trivial cluster tilting subcategories and tilted algebras of finite type.Moreover,all tilted algebras with cluster tilting subcategories are determined in te...We build a connection between iterated tilted algebras with trivial cluster tilting subcategories and tilted algebras of finite type.Moreover,all tilted algebras with cluster tilting subcategories are determined in terms of quivers.As a result,we draw the quivers of Auslander's 1-Gorenstein algebras with global dimension 2 admitting trivial cluster tilting subcategories,which implies that such algebras are of finite type but not necessarily Nakayama.展开更多
Let A be an algebra of finite Cohen-Macaulay type and F its Cohen-Macaulay Auslander algebra. We are going to characterize the morphism category Mor（∧-Gproj） of Gorenstein-projective ∧-modules in terms of the modu...Let A be an algebra of finite Cohen-Macaulay type and F its Cohen-Macaulay Auslander algebra. We are going to characterize the morphism category Mor（∧-Gproj） of Gorenstein-projective ∧-modules in terms of the module category F-mod by a categorical equivalence. Based on this, we obtain that some factor category of the epimorphism category Epi（∧-Gproj） is a Frobenius category, and also, we clarify the relations among Mor（∧-Gproj）, Mor（T2（∧）-Gproj） and Mor（△-Gproj）, where T2（∧） and △ are respectively the lower triangular matrix algebra and the Morita ring closely related to ∧.展开更多
基金Acknowledgements S.Y. Pan was supported by the National Natural Science Foundation of China （Grant No. 11201022）, the Fundamental Research Funds for the Central Universities （2013JBM096, 2013RC027）, and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education. This revision of the first draft was done when S. Y. Pan was a postdoctor of Bishop＇s University, he would like to thank Professor Thomas Briistle for his warm hospitality. X. J. Zhang was supported by National Natural Science Foundation of China （Grant No. 11101217）.
文摘Let A and B be Artin R-algebras of finite Cohen-Macaulay type. Then we prove that, if A and B are standard derived equivalent, then their Cohen-Macaulay Auslander algebras are also derived equivalent. And we show that Gorenstein projective conjecture is an invariant under standard derived equivalence between Artin R-algebras.
基金supported by the National Natural Science Foundation of China(11671230,11371165).
文摘In this article we investigate the relations between the Gorenstein projective dimensions of Λ-modules and their socles for re-minimal Auslander-Gorenstein algebras Λ.First we give a description of projective-injective Λ-modules in terms of their socles.Then we prove that a Λ-module N has Gorenstein projective dimension at most n if and only if its socle has Gorenstein projective dimension at most n if and only if N is cogenerated by a projective Λ-module.Furthermore,we show that n-minimal Auslander-Gorenstein algebras can be characterised by the relations between the Gorenstein projective dimensions of modules and their socles.
文摘We build a connection between iterated tilted algebras with trivial cluster tilting subcategories and tilted algebras of finite type.Moreover,all tilted algebras with cluster tilting subcategories are determined in terms of quivers.As a result,we draw the quivers of Auslander's 1-Gorenstein algebras with global dimension 2 admitting trivial cluster tilting subcategories,which implies that such algebras are of finite type but not necessarily Nakayama.
基金Supported by the National Natural Science Foundation of China （Grant No. 11771272）
文摘Let A be an algebra of finite Cohen-Macaulay type and F its Cohen-Macaulay Auslander algebra. We are going to characterize the morphism category Mor（∧-Gproj） of Gorenstein-projective ∧-modules in terms of the module category F-mod by a categorical equivalence. Based on this, we obtain that some factor category of the epimorphism category Epi（∧-Gproj） is a Frobenius category, and also, we clarify the relations among Mor（∧-Gproj）, Mor（T2（∧）-Gproj） and Mor（△-Gproj）, where T2（∧） and △ are respectively the lower triangular matrix algebra and the Morita ring closely related to ∧.
