Let A be a superalgebra endowed with a pseudoinvolution ∗ over an algebraically closed field of characteristic zero. If A satisfies an ordinary non-trivial identity, then its graded ∗-codimension sequence cn∗(A), n = 1,2,…, is exponentially bounded (Ioppolo and Martino (Linear Multilinear Algebra 66(11), 2286–2304 2018). In this paper we capture this exponential growth giving a positive answer to the Amitsur’s conjecture for this kind of algebras. More precisely, we shall see that the limn→∞cn∗(A)n exists and it is an integer, denoted exp ∗(A) and called graded ∗-exponent of A. Moreover, we shall characterize superalgebras with pseudoinvolution according to their graded ∗-exponent.

Ioppolo, A. (2021). A Characterization of Superalgebras with Pseudoinvolution of Exponent 2. ALGEBRAS AND REPRESENTATION THEORY, 24(6), 1415-1429 [10.1007/s10468-020-09996-4].

A Characterization of Superalgebras with Pseudoinvolution of Exponent 2

Ioppolo A.
2021

Abstract

Let A be a superalgebra endowed with a pseudoinvolution ∗ over an algebraically closed field of characteristic zero. If A satisfies an ordinary non-trivial identity, then its graded ∗-codimension sequence cn∗(A), n = 1,2,…, is exponentially bounded (Ioppolo and Martino (Linear Multilinear Algebra 66(11), 2286–2304 2018). In this paper we capture this exponential growth giving a positive answer to the Amitsur’s conjecture for this kind of algebras. More precisely, we shall see that the limn→∞cn∗(A)n exists and it is an integer, denoted exp ∗(A) and called graded ∗-exponent of A. Moreover, we shall characterize superalgebras with pseudoinvolution according to their graded ∗-exponent.
Articolo in rivista - Articolo scientifico
Exponent; Exponential growth; Polynomial identities; Pseudoinvolutions;
English
22-set-2020
2021
24
6
1415
1429
reserved
Ioppolo, A. (2021). A Characterization of Superalgebras with Pseudoinvolution of Exponent 2. ALGEBRAS AND REPRESENTATION THEORY, 24(6), 1415-1429 [10.1007/s10468-020-09996-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/314261
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