Graded polynomial identities and codimensions: Computing the exponential growth |
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Authors: | A Giambruno D La Mattina |
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Institution: | Dipartimento di Matematica e Informatica, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy |
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Abstract: | Let G be a finite abelian group and A a G-graded algebra over a field of characteristic zero. This paper is devoted to a quantitative study of the graded polynomial identities satisfied by A. We study the asymptotic behavior of , n=1,2,…, the sequence of graded codimensions of A and we prove that if A satisfies an ordinary polynomial identity, exists and is an integer. We give an explicit way of computing such integer by proving that it equals the dimension of a suitable finite dimension semisimple G×Z2-graded algebra related to A. |
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Keywords: | 16R10 16W50 16P90 |
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