Graded polynomial identities and codimensions: computing the exponential growth
By Antonio Giambruno, D. La Mattina. 2010
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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 c n G ( A ) , n = 1 , 2 , … , the sequence of graded codimensions of A and we prove that if A satisfies an ordinary polynomial identity, lim n → ∞ c n G ( A ) n 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 × Z 2 -graded algebra related to A.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/006e8c34ccf11feadff162dffa097c24844212fe
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Citations in the corpus
- Amitsur's conjecture for associative algebras with a generalized Hopf action (2012, background): “[13] Giambruno, A., La Mattina, D. Graded polynomial identities and codimensions: computing the expo- nential growth.”