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# Generalized Commutativity in Group Algebras

Published:2003-03-01
Printed: Mar 2003
• Yu. A. Bahturin
• M. M. Parmenter
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## Abstract

We study group algebras $FG$ which can be graded by a finite abelian group $\Gamma$ such that $FG$ is $\beta$-commutative for a skew-symmetric bicharacter $\beta$ on $\Gamma$ with values in $F^*$.
 MSC Classifications: 16S34 - Group rings [See also 20C05, 20C07], Laurent polynomial rings 16R50 - Other kinds of identities (generalized polynomial, rational, involution) 16U80 - Generalizations of commutativity 16W10 - Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx] 16W55 - Super'' (or skew'') structure [See also 17A70, 17Bxx, 17C70] {For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66}

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