Asymptotic behaviour of codimensions of p. i. algebras satisfying Capelli identities

Berele, Allan; Regev, Amitai

doi:10.1090/S0002-9947-08-04500-5

Asymptotic behaviour of codimensions of p. i. algebras satisfying Capelli identities
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Trans. Amer. Math. Soc. 360 (2008), 5155-5172 Request permission

Abstract:

Let $A$ be a p. i. algebra with 1 in characteristic zero, satisfying a Capelli identity. Then the cocharacter sequence $c_n(A)$ is asymptotic to a function of the form $an^g\ell ^n$, where $\ell \in \mathbb {N}$ and $g \in \mathbb {Z}$.

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