Geodesic
Group Gradings on Associative Algebras with Involution
Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 182-194

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we describe the group gradings by a finite abelian group $G$ of the matrix algebra ${{M}_{n}}(F)$ over an algebraically closed field $F$ of characteristic different from 2, which respect an involution (involution gradings). We also describe, under somewhat heavier restrictions on the base field, all $G$ -gradings on all finite-dimensional involution simple algebras.
DOI : 10.4153/CMB-2008-020-7
Mots-clés : 16W10, 16W50 
Bahturin, Y. A.; Giambruno, A. Group Gradings on Associative Algebras with Involution. Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 182-194. doi: 10.4153/CMB-2008-020-7
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[1] [1] Bahturin, Y., Sehgal, S., and Zaicev, M., Group gradings on associative algebras. J. Algebra, 241(2001), no. 2677–698. Google Scholar

[2] [2] Bahturin, Y. and Shestakov, I., Gradings of simple Jordan algebras and their relation to the gradings of simple associative algebras. Comm. Algebra, 999(2002), 111–222. Google Scholar

[3] [3] Bahturin, Y., Shestakov, I. and Zaicev, M., Gradings on simple Jordan and Lie algebras. J. Algebra 283(2005), no. 2, 849–868. Google Scholar

[4] [4] Bahturin, Y. amd Zaicev, M., Involutions on graded matrix algebras. J. Algebra 315(2007), no. 2, 527–540. Google Scholar

[5] [5] Bahturin, Y. amd Zaicev, M., Graded algebras and graded identities. In: Polynomial Identities and Combinatorial Methods. Lecture Notes in Pure and Appl. Math. 235, Dekker, New York, 2003, pp. 101–139. Google Scholar

[6] [6] Bahturin, Y. amd Zaicev, M., Group gradings on matrix algebras. Canad. Math. Bull. 45(2002), no. 4, 499–508. Google Scholar

[7] [7] Bahturin, Y. amd Zaicev, M., Gradings on Simple Lie Algebras of Type “A”. J. Lie Theory 16(2006), no. 4, 719–742. Google Scholar

[8] [8] Rowen, L. H., Polynomial Identities in Ring Theory. Pure and Applied Mathematics 84, Academic Press, New York, 1980. Google Scholar

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