Standard polynomials and matrices with superinvolutions

Antonino Giambruno, Fabrizio Martino, Antonio Ioppolo, Fabrizio Martino

Risultato della ricerca: Article

6 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
RivistaDefault journal
Volume504
Stato di pubblicazionePublished - 2016

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Skew symmetric matrix
Polynomial Identities
Transpose
Codimension
Polynomials
Generator
Algebra
Polynomial
Subset
Zero
Set theory
Standards

All Science Journal Classification (ASJC) codes

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

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Giambruno, A., Martino, F., Ioppolo, A., & Martino, F. (2016). Standard polynomials and matrices with superinvolutions. Default journal, 504, 272-291.

Standard polynomials and matrices with superinvolutions. / Giambruno, Antonino; Martino, Fabrizio; Ioppolo, Antonio; Martino, Fabrizio.

In: Default journal, Vol. 504, 2016, pag. 272-291.

Risultato della ricerca: Article

Giambruno, A, Martino, F, Ioppolo, A & Martino, F 2016, 'Standard polynomials and matrices with superinvolutions', Default journal, vol. 504, pagg. 272-291.
Giambruno A, Martino F, Ioppolo A, Martino F. Standard polynomials and matrices with superinvolutions. Default journal. 2016;504:272-291.
Giambruno, Antonino ; Martino, Fabrizio ; Ioppolo, Antonio ; Martino, Fabrizio. / Standard polynomials and matrices with superinvolutions. In: Default journal. 2016 ; Vol. 504. pagg. 272-291.
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AU - Giambruno, Antonino

AU - Martino, Fabrizio

AU - Ioppolo, Antonio

AU - Martino, Fabrizio

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Algebra and Number Theory

KW - Discrete Mathematics and Combinatorics

KW - Geometry and Topology

KW - Minimal degree

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KW - Polynomial identity

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JO - Default journal

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