Standard polynomials and matrices with superinvolutions
- Autori: Giambruno, A.; Ioppolo, A.; Martino, F.
- Anno di pubblicazione: 2016
- Tipologia: Articolo in rivista (Articolo in rivista)
- Parole Chiave: Minimal degree; Polynomial identity; Superinvolution; Algebra and Number Theory; Numerical Analysis; Geometry and Topology; Discrete Mathematics and Combinatorics
- OA Link: http://hdl.handle.net/10447/219025
Abstract
Let Mn(F) be the algebra of n x n matrices over a field F of characteristic zero. The superinvolutions ∗ on Mn(F) were classified by Racine in [12]. They are of two types, the transpose and the orthosymplectic superinvolution. This paper is devoted to the study of ∗-polynomial identities satisfied by Mn(F). The goal is twofold. On one hand, we determine the minimal degree of a standard polynomial vanishing on suitable subsets of symmetric or skew-symmetric matrices for both types of superinvolutions. On the other, in case of M2(F), we find generators of the ideal of ∗-identities and we compute the corresponding sequences of cocharacters and codimensions.