Periodic algebras which are almost Koszul

S Brenner; M C R Butler; Alastair D King

doi:10.1023/A:1020146502185

Periodic algebras which are almost Koszul

S Brenner, M C R Butler, Alastair D King

Department of Mathematical Sciences

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

86 Citations (SciVal)

Abstract

The preprojective algebra and the trivial extension algebra of a Dynkin quiver (in bipartite orientation) are very close to being a Koszul dual pair of algebras. In this case the usual duality theory may be adapted to show that each algebra has a periodic bimodule resolution built using the other algebra and some extra data: an algebra automorphism. A general theory of such lsquoalmost Koszulrsquo algebras is developed and other examples are given.

Original language	English
Pages (from-to)	331-368
Number of pages	38
Journal	Algebras and Representation Theory
Volume	5
Issue number	4
DOIs	https://doi.org/10.1023/A:1020146502185
Publication status	Published - Oct 2002

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10.1023/A:1020146502185

Cite this

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title = "Periodic algebras which are almost Koszul",

abstract = "The preprojective algebra and the trivial extension algebra of a Dynkin quiver (in bipartite orientation) are very close to being a Koszul dual pair of algebras. In this case the usual duality theory may be adapted to show that each algebra has a periodic bimodule resolution built using the other algebra and some extra data: an algebra automorphism. A general theory of such lsquoalmost Koszulrsquo algebras is developed and other examples are given.",

author = "S Brenner and Butler, {M C R} and King, {Alastair D}",

year = "2002",

month = oct,

doi = "10.1023/A:1020146502185",

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pages = "331--368",

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AU - Brenner, S

AU - Butler, M C R

AU - King, Alastair D

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N2 - The preprojective algebra and the trivial extension algebra of a Dynkin quiver (in bipartite orientation) are very close to being a Koszul dual pair of algebras. In this case the usual duality theory may be adapted to show that each algebra has a periodic bimodule resolution built using the other algebra and some extra data: an algebra automorphism. A general theory of such lsquoalmost Koszulrsquo algebras is developed and other examples are given.

AB - The preprojective algebra and the trivial extension algebra of a Dynkin quiver (in bipartite orientation) are very close to being a Koszul dual pair of algebras. In this case the usual duality theory may be adapted to show that each algebra has a periodic bimodule resolution built using the other algebra and some extra data: an algebra automorphism. A general theory of such lsquoalmost Koszulrsquo algebras is developed and other examples are given.

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U2 - 10.1023/A:1020146502185

DO - 10.1023/A:1020146502185

M3 - Article

SN - 1572-9079

VL - 5

SP - 331

EP - 368

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 4

ER -

Periodic algebras which are almost Koszul

Abstract

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