6533b870fe1ef96bd12cfb1c
RESEARCH PRODUCT
Involution Codimensions of Finite Dimensional Algebras and Exponential Growth
Mikhail ZaicevAntonino Giambrunosubject
Discrete mathematicsInvolution (mathematics)Pure mathematicsAlgebra and Number TheoryExponential growthMathematicsdescription
Abstract 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 ∗ -codimensions c n ( A , ∗ ) of A and we show that Exp(A, ∗ ) = lim n → ∞ c n ( A , ∗ ) 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 ∗ -simple if and only if Exp( A , ∗ ) = dim F A .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1999-12-01 | Journal of Algebra |