Separable deformations of the generalized quaternion group algebras

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The group algebras kQ2n {kQ-{2{n}}} of the generalized quaternion groups Q 2 n {Q-{2{n}}} over fields k which contain 2 n - 2 {\mathbb{F}-{2{n-2}}} are deformed to separable k ((t)) {k((t))}-algebras [kQ 2 n] t {[kQ-{2{n}}]-{t}}. The dimensions of the simple components of k((t)) Š - k ((t)) [ k Q 2 n ] t {\overline{k((t))}\otimes-{k((t))}[kQ-{2{n}}]-{t}} over the algebraic closure k ((t)) {\overline{k((t))}}, and those of Q 2 n {\mathbb{C}Q-{2{n}}} over {\mathbb{C}} are the same, yielding strong solutions of the Donald-Flanigan conjecture for the generalized quaternion groups.

Original languageEnglish
Pages (from-to)179–191
JournalJournal of Group Theory
StatePublished - 2019

Bibliographical note

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

ASJC Scopus subject areas

  • Algebra and Number Theory


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