Homological properties of piecewise hereditary algebras

Dieter Happel; Dan Zacharia

doi:10.1016/j.jalgebra.2009.11.020

Homological properties of piecewise hereditary algebras

Dieter Happel, Dan Zacharia

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Let Λ be a finite dimensional algebra over an algebraically closed field k. We will investigate homological properties of piecewise hereditary algebras Λ. In particular we give lower and upper bounds of the strong global dimension, show the behavior of the strong global dimension under one point extensions and tilting. Moreover we show that the "pieces" of modΛ have Auslander-Reiten sequences.

Original language	English (US)
Pages (from-to)	1139-1154
Number of pages	16
Journal	Journal of Algebra
Volume	323
Issue number	4
DOIs	https://doi.org/10.1016/j.jalgebra.2009.11.020
State	Published - Feb 15 2010

Keywords

Homological algebra
Representations of algebras

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2009.11.020

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title = "Homological properties of piecewise hereditary algebras",

abstract = "Let Λ be a finite dimensional algebra over an algebraically closed field k. We will investigate homological properties of piecewise hereditary algebras Λ. In particular we give lower and upper bounds of the strong global dimension, show the behavior of the strong global dimension under one point extensions and tilting. Moreover we show that the {"}pieces{"} of modΛ have Auslander-Reiten sequences.",

keywords = "Homological algebra, Representations of algebras",

author = "Dieter Happel and Dan Zacharia",

note = "Funding Information: ✩ The second author is supported by a grant from NSA. Most of these results were obtained during a stay in Oberwolfach as part of the Research in Pairs program. We thank the Mathematics Institute in Oberwolfach for making this stay possible. * Corresponding author. E-mail addresses: [email protected] (D. Happel), [email protected] (D. Zacharia).",

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AU - Happel, Dieter

AU - Zacharia, Dan

N1 - Funding Information: ✩ The second author is supported by a grant from NSA. Most of these results were obtained during a stay in Oberwolfach as part of the Research in Pairs program. We thank the Mathematics Institute in Oberwolfach for making this stay possible. * Corresponding author. E-mail addresses: [email protected] (D. Happel), [email protected] (D. Zacharia).

PY - 2010/2/15

Y1 - 2010/2/15

N2 - Let Λ be a finite dimensional algebra over an algebraically closed field k. We will investigate homological properties of piecewise hereditary algebras Λ. In particular we give lower and upper bounds of the strong global dimension, show the behavior of the strong global dimension under one point extensions and tilting. Moreover we show that the "pieces" of modΛ have Auslander-Reiten sequences.

AB - Let Λ be a finite dimensional algebra over an algebraically closed field k. We will investigate homological properties of piecewise hereditary algebras Λ. In particular we give lower and upper bounds of the strong global dimension, show the behavior of the strong global dimension under one point extensions and tilting. Moreover we show that the "pieces" of modΛ have Auslander-Reiten sequences.

KW - Homological algebra

KW - Representations of algebras

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DO - 10.1016/j.jalgebra.2009.11.020

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SP - 1139

EP - 1154

JO - Journal of Algebra

JF - Journal of Algebra

IS - 4

ER -

Homological properties of piecewise hereditary algebras

Abstract

Keywords

ASJC Scopus subject areas

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