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Deformed mesh algebras of Dynkin type ℂₙ

Jerzy Białkowski, Karin Erdmann, Andrzej Skowroński (2012)

Colloquium Mathematicae

In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type ₙ (in the sense of our earlier work in Trans. Amer Math. Soc. 359 (2007)) are exactly (up to isomorphism) the stable Auslander algebras of simple plane singularities of Dynkin type 2 n . In this article we complete the picture by showing that the deformed mesh algebras of Dynkin type ℂₙ are isomorphic to the canonical mesh algebras of type ℂₙ, and hence to the stable Auslander algebras...

Derived endo-discrete artin algebras

Raymundo Bautista (2006)

Colloquium Mathematicae

Let Λ be an artin algebra. We prove that for each sequence ( h i ) i of non-negative integers there are only a finite number of isomorphism classes of indecomposables X b ( Λ ) , the bounded derived category of Λ, with l e n g t h E ( X ) H i ( X ) = h i for all i ∈ ℤ and E(X) the endomorphism ring of X in b ( Λ ) if and only if b ( M o d Λ ) , the bounded derived category of the category M o d Λ of all left Λ-modules, has no generic objects in the sense of [4].

Derived equivalence classification of weakly symmetric algebras of domestic type

Rafał Bocian, Andrzej Skowroński (2016)

Colloquium Mathematicae

We complete the derived equivalence classification of all weakly symmetric algebras of domestic type over an algebraically closed field, by solving the problem of distinguishing standard and nonstandard algebras up to stable equivalence, and hence derived equivalence. As a consequence, a complete stable equivalence classification of weakly symmetric algebras of domestic type is obtained.

Diagonal reductions of matrices over exchange ideals

Huanyin Chen (2006)

Czechoslovak Mathematical Journal

In this paper, we introduce related comparability for exchange ideals. Let I be an exchange ideal of a ring R . If I satisfies related comparability, then for any regular matrix A M n ( I ) , there exist left invertible U 1 , U 2 M n ( R ) and right invertible V 1 , V 2 M n ( R ) such that U 1 V 1 A U 2 V 2 = diag ( e 1 , , e n ) for idempotents e 1 , , e n I .

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