Let k be an algebraically closed field, ∧ a finite dimensional k-algebra. According to Morita equivalence, we can always assume that ∧ is basic and connected. We denote by mod∧ the category of all finite generated ...Let k be an algebraically closed field, ∧ a finite dimensional k-algebra. According to Morita equivalence, we can always assume that ∧ is basic and connected. We denote by mod∧ the category of all finite generated left ∧-modules, and by F<sub>∧</sub> the Auslander-Reiten quiver of A. Let P<sub>1</sub>, P<sub>2</sub>,…, P<sub>n</sub> be all the indecomposable projective modules up to isomorphism. For any module M ∈ mod∧, its dimension vector is defined展开更多
Using the connection between McKay quiver and Loewy matrix, and the properties of characteristic polynomial of Loewy matrix, we give a generalized way to determine the McKay quiver for a finite subgroup of a generaliz...Using the connection between McKay quiver and Loewy matrix, and the properties of characteristic polynomial of Loewy matrix, we give a generalized way to determine the McKay quiver for a finite subgroup of a generalized linear group.展开更多
Let T(A)=A?D(A) be a representation-finite trivial extension algebra. We haveproved: (i) every indecomposable module of T(A) is determined by its top and socle, (ii)every indecomposable module of T(A) is determined by...Let T(A)=A?D(A) be a representation-finite trivial extension algebra. We haveproved: (i) every indecomposable module of T(A) is determined by its top and socle, (ii)every indecomposable module of T(A) is determined by its Loewy factors and socal factorsrespectively.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘Let k be an algebraically closed field, ∧ a finite dimensional k-algebra. According to Morita equivalence, we can always assume that ∧ is basic and connected. We denote by mod∧ the category of all finite generated left ∧-modules, and by F<sub>∧</sub> the Auslander-Reiten quiver of A. Let P<sub>1</sub>, P<sub>2</sub>,…, P<sub>n</sub> be all the indecomposable projective modules up to isomorphism. For any module M ∈ mod∧, its dimension vector is defined
基金Foundation item:This work is partly supported by NSF(103710036)of Chinakey project(02A024)of provincial Ministry of Foundation of Hunan.
文摘Using the connection between McKay quiver and Loewy matrix, and the properties of characteristic polynomial of Loewy matrix, we give a generalized way to determine the McKay quiver for a finite subgroup of a generalized linear group.
基金Project supported by the National Natural Science Foundation of China.
文摘Let T(A)=A?D(A) be a representation-finite trivial extension algebra. We haveproved: (i) every indecomposable module of T(A) is determined by its top and socle, (ii)every indecomposable module of T(A) is determined by its Loewy factors and socal factorsrespectively.
