The Asymptotic Behavior of the Codimension Sequence of Affine G - Graded Algebras

2015/04/01 by Shpigelman, Yuval
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1504.00373

Abstract

Let W be an affine PI algebra over a field of characteristic zero graded by a finite group G. We show that there exist α₁,α₂∈ℝ, β∈(1)/(2)ℤ, and l∈ℕ such that α₁n^βlⁿ≤ c_n^G(W)≤α₂n^βlⁿ. Furthermore, if W has a unit then the asymptotic behavior of c_n^G(W) is αn^βlⁿ where α∈ℝ, β∈(1)/(2)ℤ, l∈ℕ.

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