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Generalized Commutativity in Group Algebras

Published online by Cambridge University Press:  20 November 2018

Yu. A. Bahturin  and
M. M. Parmenter
Yu. A. Bahturin
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, A1C 5S7
M. M. Parmenter
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, A1C 5S7
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Abstract

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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 ${{F}^{*}}$.

Keywords

16S3416R5016U8016W1016W55
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 1 , 01 March 2003 , pp. 14 - 25
Copyright
Copyright © Canadian Mathematical Society 2003

References

[BC] Bergen, J. and Cohen, M., Actions of commutative Hopf algebras. Bull. LondonMath. Soc. 18 (1986), 159–164.Google Scholar
[BFM] Bahturin, Yu. A., Fischman, D. and Montgomery, S., On the generalized Lie structure of associative algebras. Israel J. Math. 96 (1996), 27–48.Google Scholar
[BSZ] Bahturin, Yu. A., Sehgal, S. K. and Zaicev, M. V., Group gradings on associative algebras, J. Algebra, to appear.Google Scholar
[BZ] Bahturin, Yu. A. and Zaicev, M. V., Identities of graded algebras. J. Algebra 205 (1998), 1–12.Google Scholar
[Jac] Jacobson, N., Lie Algebras. Wiley-Interscience, New York, 1962.Google Scholar
[Jen] Jennings, S. A., The structure of the group ring of a p-group over a modular field. Trans. Amer. Math. Soc. 50 (1941), 175–185.Google Scholar
[P] Passman, D. S., The Algebraic Structure of Group Rings. Wiley-Interscience, New York, 1977.Google Scholar
[ZS] Zaicev, M. V. and Sehgal, S. K., Finite gradings of simple Artinian Rings. Vestnik Moskov. Univ. Ser. I Mat. Mekh., to appear.Google Scholar