Semi-invariant matrices over finite groups

Yuval Ginosar; Ofir Schnabel

doi:10.1007/s10468-012-9394-7

Semi-invariant matrices over finite groups

Yuval Ginosar, Ofir Schnabel

Department of Mathematics

University of Haifa

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

Abstract

The semi-center of an artinian semisimple module-algebra over a finite group G can be described using the projective representations of G. In particular, the semi-center of the endomorphism ring of an irreducible projective representation over an algebraically closed field has a structure of a twisted group algebra. The following group-theoretic result is deduced: the center of a group of central type embeds into the group of its linear characters.

Original language	American English
Pages (from-to)	199-212
Number of pages	14
Journal	Algebras and Representation Theory
Volume	17
Issue number	1
DOIs	https://doi.org/10.1007/s10468-012-9394-7
State	Published - Feb 2014

Keywords

Projective representation
Semi-invariants
Twisted group algebra

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s10468-012-9394-7

Cite this

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title = "Semi-invariant matrices over finite groups",

abstract = "The semi-center of an artinian semisimple module-algebra over a finite group G can be described using the projective representations of G. In particular, the semi-center of the endomorphism ring of an irreducible projective representation over an algebraically closed field has a structure of a twisted group algebra. The following group-theoretic result is deduced: the center of a group of central type embeds into the group of its linear characters.",

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AU - Schnabel, Ofir

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N2 - The semi-center of an artinian semisimple module-algebra over a finite group G can be described using the projective representations of G. In particular, the semi-center of the endomorphism ring of an irreducible projective representation over an algebraically closed field has a structure of a twisted group algebra. The following group-theoretic result is deduced: the center of a group of central type embeds into the group of its linear characters.

AB - The semi-center of an artinian semisimple module-algebra over a finite group G can be described using the projective representations of G. In particular, the semi-center of the endomorphism ring of an irreducible projective representation over an algebraically closed field has a structure of a twisted group algebra. The following group-theoretic result is deduced: the center of a group of central type embeds into the group of its linear characters.

KW - Projective representation

KW - Semi-invariants

KW - Twisted group algebra

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U2 - 10.1007/s10468-012-9394-7

DO - 10.1007/s10468-012-9394-7

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EP - 212

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 1

ER -

Semi-invariant matrices over finite groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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