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Involution Codimensions of Finite Dimensional Algebras and Exponential Growth

✍ Scribed by A Giambruno; M Zaicev

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
114 KB
Volume
222
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let F be a field of characteristic zero and let A be a finite dimensional algebra with involution ) over F. We study the asymptotic behavior of the sequence of n Ε½ . Ε½ . )-codimensions c A, ) of A and we show that Exp A, ) s lim c A, )

' Ε½ .

n n Βͺ Ο± n Ε½ . exists and is an integer. We give an explicit way for computing Exp A, ) and as a consequence we obtain the following characterization of )-simple algebras: A is Ε½ . )-simple if and only if Exp A, ) s dim A.

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Let A be a PI-algebra over a field F. We study the asymptotic behavior of the sequence of codimensions c n (A) of A. We show that if A is finitely generated over F then Inv(A)=lim n Γ„ n c n (A) always exists and is an integer. We also obtain the following characterization of simple algebras: A is fi