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arXiv · 1504.00373

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

Yuval Shpigelman
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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 $α_{1},α_{2}\in\mathbb{R}, β\in\frac{1}{2}\mathbb{Z}$, and $l\in\mathbb{N}$ such that $α_{1}n^βl^{n}\leq c_{n}^{G}(W)\leqα_{2}n^βl^{n}$. Furthermore, if W has a unit then the asymptotic behavior of $c_{n}^{G}(W)$ is $αn^βl^{n}$ where $α\in\mathbb{R}, β\in\frac{1}{2}\mathbb{Z}, l\in\mathbb{N}$.

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Yuval Shpigelman. 2015-04-01. The Asymptotic Behavior of the Codimension Sequence of Affine G - Graded Algebras. https://arxiv.org/abs/1504.00373

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