Superalgebras with superinvolution or graded involution with colengths sequence bounded by 3

Author(s)

Ioppolo, Antonio ^[1]

Affiliation

^[1] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION; v. 30, n. 4, p. 821-838, JUN 2020.
• Web of Science Citations: 0

Abstract

Let A be a superalgebra with superinvolution or graded involution over a field of characteristic zero and let chi(n1, ..., n4) (A), n(1)+ ...+ n(4) = n, be the (n(1), ..., n(4))-cocharacter of A. The ({*})-colengths sequence, l(n){*}(A), n = 1, 2, ..., is the sum of the multiplicities in the decomposition of the (n(1), ..., n(4))-cocharacter chi(n1, ..., n4) (A), for all n = n(1)+...+n(4) >= 1. The main purpose of this paper is to classify the superalgebras with superinvolution with ({*})-colengths sequence bounded by three. Moreover, we shall extend to the general case, the analogous result proved by do Nascimento and Vieira in {[}Superalgebras with graded involution and star-graded colength bounded by 3, Linear Multilinear Algebra 67(10) (2019) 1999-2020] for finite-dimensional superalgebras with graded involution. (AU)

• FAPESP's process: 18/17464-3 - Polynomial identities and superinvolutions
• Grantee: Antonio Ioppolo
• Support Opportunities: Scholarships in Brazil - Post-Doctoral