Non-principal blocks with one simple module

David John Benson; Edward L.  Green

doi:10.1093/qmath/hag039

Non-principal blocks with one simple module

David John Benson, Edward L. Green

Mathematical Science

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

15 Citations (Scopus)

Abstract

We give a general construction which shows that a large class of quantum complete intersections can be realized as the basic algebras of non-principal blocks of finite groups. We investigate the Ext rings of these algebras. We describe how to construct a finite p'-covering for one of these quantum complete intersections, which supports a Hopf algebra structure which is neither commutative nor cocommutative in general. We use this to investigate a problem concerning the definition of nucleus for a non-principal block.

Original language	English
Pages (from-to)	1-11
Number of pages	10
Journal	Quarterly Journal of Mathematics
Volume	55
Issue number	1
DOIs	https://doi.org/10.1093/qmath/hag039
Publication status	Published - 2004

Keywords

quantum groups
algebras
varieties
cohomology
coverings

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10.1093/qmath/hag039

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AB - We give a general construction which shows that a large class of quantum complete intersections can be realized as the basic algebras of non-principal blocks of finite groups. We investigate the Ext rings of these algebras. We describe how to construct a finite p'-covering for one of these quantum complete intersections, which supports a Hopf algebra structure which is neither commutative nor cocommutative in general. We use this to investigate a problem concerning the definition of nucleus for a non-principal block.

KW - quantum groups

KW - algebras

KW - varieties

KW - cohomology

KW - coverings

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DO - 10.1093/qmath/hag039

M3 - Article

SN - 0033-5606

VL - 55

SP - 1

EP - 11

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 1

ER -

Non-principal blocks with one simple module

Abstract

Keywords

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