Exponential Codimension Growth of PI Algebras: An Exact Estimate

Authors: Giambruno A.¹; Zaicev M.²

Source: Advances in Mathematics, Volume 142, Number 2, March 1999 , pp. 221-243(23)

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Abstract:

Let A be an associative PI-algebra over a field F of characteristic zero. By studying the exponential behavior of the sequence of codimensions {c_n(A)} of A, we prove that Inv(A)=lim_n nc_n(A) always exists and is an integer. We also give an explicit way for computing such integer: let B be a finite dimensional Z₂-graded algebra whose Grassmann envelope G(B) satisfies the same identities of A; then Inv(A)=Inv(G(B))=dim C⁽⁰⁾+dim C⁽¹⁾ where C⁽⁰⁾+C⁽¹⁾ is a suitable Z₂-graded semisimple subalgebra of B. Copyright 1999 Academic Press.

Language: English

Document Type: Research article

Affiliations: 1: Dipartimento di Matematica e Applicazioni, Università di Palermo, Palermo, 90123, Italy 2: Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia

Publication date: 1999-03-01