Geodesic
Codimensions of generalized polynomial identities
Sbornik. Mathematics, Tome 201 (2010) no. 2, pp. 235-251 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that for every finite-dimensional associative algebra $A$ over a field of characteristic zero there are numbers $C\in\mathbb Q_+$ and $t\in\mathbb Z_+$ such that $gc_n(A)\sim Cn^td^n$ as $n\to\infty$, where $d=PI\exp(A)\in\mathbb Z_+$. Thus, Amitsur's and Regev's conjectures hold for the codimensions $gc_n(A)$ of the generalized polynomial identities. Bibliography: 6 titles.
Keywords: associative algebra, generalized polynomial identity, asymptotic behaviour of codimensions, $PI$-exponent, representation of a symmetric group. 
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A. S. Gordienko. Codimensions of generalized polynomial identities. Sbornik. Mathematics, Tome 201 (2010) no. 2, pp. 235-251. http://geodesic.mathdoc.fr/item/SM_2010_201_2_a2/

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