Can one compute the exponential rate of growth of the ∗-codimensions of a PI-algebra with involution ∗ over a field of characteristic zero? It was shown ithat any such algebra A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution B. Here, by exploiting this result we are able to provide an exact estimate of the exponential rate of growth exp∗(A) of any PI-algebra A with involution. It turns out that exp∗(A) is an integer and, in case the base field is algebraically closed, it coincides with the dimension of an admissible subalgebra of maximal dimension of B.

Giambruno, A., Polcino Milies, C., Valenti, A. (2017). Star-polynomial identities: Computing the exponential growth of the codimensions. JOURNAL OF ALGEBRA, 469, 302-322 [10.1016/j.jalgebra.2016.07.037].

Star-polynomial identities: Computing the exponential growth of the codimensions

GIAMBRUNO, Antonino
;
VALENTI, Angela
2017-01-01

Abstract

Can one compute the exponential rate of growth of the ∗-codimensions of a PI-algebra with involution ∗ over a field of characteristic zero? It was shown ithat any such algebra A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution B. Here, by exploiting this result we are able to provide an exact estimate of the exponential rate of growth exp∗(A) of any PI-algebra A with involution. It turns out that exp∗(A) is an integer and, in case the base field is algebraically closed, it coincides with the dimension of an admissible subalgebra of maximal dimension of B.
Settore MAT/02 - Algebra
https://www.sciencedirect.com/science/article/pii/S0021869316302800?via=ihub
Giambruno, A., Polcino Milies, C., Valenti, A. (2017). Star-polynomial identities: Computing the exponential growth of the codimensions. JOURNAL OF ALGEBRA, 469, 302-322 [10.1016/j.jalgebra.2016.07.037].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/219217
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