The extension dimension of triangular matrix algebras

For any positive integer [Formula: see text], we clearly describe all finite-dimensional algebras [Formula: see text] such that the upper triangular matrix algebras [Formula: see text] are piecewise hereditary. Consequently, we describe all finite-dimensional algebras [Formula: see text] such that their derived categories of [Formula: see text]-complexes are triangulated equivalent to derived categories of hereditary abelian categories, and we describe the tensor algebras [Formula: see text] for which their singularity categories are triangulated orbit categories of the derived categories of hereditary abelian categories.

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Gorenstein Projective Modules over Triangular Matrix Rings

Algebra Colloquium ◽

10.1142/s1005386716000122 ◽

2016 ◽

Vol 23 (01) ◽

pp. 97-104 ◽

Cited By ~ 1

Author(s):

H. Eshraghi ◽

R. Hafezi ◽

Sh. Salarian ◽

Z. W. Li

Keyword(s):

Triangular Matrix ◽

Projective Modules ◽

Matrix Rings ◽

Matrix Algebras ◽

Gorenstein Projective Modules ◽

Artin Algebras ◽

Acyclic Complexes ◽

Matrix Extension

Let R and S be Artin algebras and Γ be their triangular matrix extension via a bimodule SMR. We study totally acyclic complexes of projective Γ-modules and obtain a complete description of Gorenstein projective Γ-modules. We then construct some examples of Cohen-Macaulay finite and virtually Gorenstein triangular matrix algebras.

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Graded involutions on block-triangular matrix algebras

Linear Algebra and its Applications ◽

10.1016/j.laa.2019.09.023 ◽

2020 ◽

Vol 585 ◽

pp. 24-44

Author(s):

Claudemir Fidelis ◽

Dimas José Gonçalves ◽

Diogo Diniz ◽

Felipe Yukihide Yasumura

Keyword(s):

Triangular Matrix ◽

Matrix Algebras ◽

Block Triangular Matrix

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Abelian Gradings on Upper Block Triangular Matrices

Canadian Mathematical Bulletin ◽

10.4153/cmb-2011-048-4 ◽

2012 ◽

Vol 55 (1) ◽

pp. 208-213 ◽

Cited By ~ 10

Author(s):

Angela Valenti ◽

Mikhail Zaicev

Keyword(s):

Abelian Group ◽

Characteristic Zero ◽

Finite Abelian Group ◽

Triangular Matrix ◽

Closed Field ◽

Triangular Matrices ◽

Algebraically Closed Field ◽

Matrix Algebras ◽

Block Triangular Matrix

AbstractLet G be an arbitrary finite abelian group. We describe all possible G-gradings on upper block triangular matrix algebras over an algebraically closed field of characteristic zero.

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