Standard polynomials and matrices with superinvolutions

Antonino Giambruno, Fabrizio Martino, Fabrizio Martino, Antonio Ioppolo

Risultato della ricerca: Article

7 Citazioni (Scopus)

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.
Lingua originaleEnglish
pagine (da-a)272-291
Numero di pagine20
RivistaLinear Algebra and Its Applications
Volume504
Stato di pubblicazionePublished - 2016

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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