Separable deformations of the generalized quaternion group algebras

Yuval Ginosar

doi:10.1515/jgth-2019-0042

Separable deformations of the generalized quaternion group algebras

Yuval Ginosar

Department of Mathematics

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

Abstract

The group algebras kQ₂n of the generalized quaternion groups Q₂n over fields k which contain F₂n-2 are deformed to separable k..t//-algebras ŒkQ₂n]_t. The dimensions of the simple components of k..t// ☉_k..t// ŒkQ₂n]_t over the algebraic closure k..t//, and those of CQ₂n over C are the same, yielding strong solutions of the Donald–Flanigan conjecture for the generalized quaternion groups.

Original language	English
Pages (from-to)	179–191
Number of pages	13
Journal	Journal of Group Theory
Volume	23
Issue number	1
DOIs	https://doi.org/10.1515/jgth-2019-0042
State	Published - 2019

Bibliographical note

Publisher Copyright:
© 2019 Walter de Gruyter GmbH, Berlin/Boston.

ASJC Scopus subject areas

Algebra and Number Theory

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10.1515/jgth-2019-0042

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title = "Separable deformations of the generalized quaternion group algebras",

abstract = "The group algebras kQ2n of the generalized quaternion groups Q2n over fields k which contain F2n-2 are deformed to separable k..t//-algebras {\OE}kQ2n]t. The dimensions of the simple components of k..t// ☉k..t// {\OE}kQ2n]t over the algebraic closure k..t//, and those of CQ2n over C are the same, yielding strong solutions of the Donald–Flanigan conjecture for the generalized quaternion groups.",

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AB - The group algebras kQ2n of the generalized quaternion groups Q2n over fields k which contain F2n-2 are deformed to separable k..t//-algebras ŒkQ2n]t. The dimensions of the simple components of k..t// ☉k..t// ŒkQ2n]t over the algebraic closure k..t//, and those of CQ2n over C are the same, yielding strong solutions of the Donald–Flanigan conjecture for the generalized quaternion groups.

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DO - 10.1515/jgth-2019-0042

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Separable deformations of the generalized quaternion group algebras

Abstract

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