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Exponential Codimension Growth of PI Algebras: An Exact Estimate

✍ Scribed by A Giambruno; M Zaicev

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 235 KB
Volume: 142
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1998.1790

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✦ Synopsis

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 Ä n c n (A) always exists and is an integer. We also give an explicit way for computing such integer: let B be a finite dimensional Z 2 -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 Z 2 -graded semisimple subalgebra of B.

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