### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 272-291 |

Numero di pagine | 20 |

Rivista | Default journal |

Volume | 504 |

Stato di pubblicazione | Published - 2016 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cita questo

*Default journal*,

*504*, 272-291.

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

Risultato della ricerca: Article

*Default journal*, vol. 504, pagg. 272-291.

}

TY - JOUR

T1 - Standard polynomials and matrices with superinvolutions

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

KW - Numerical Analysis

KW - Polynomial identity

KW - Superinvolution

UR - http://hdl.handle.net/10447/219025

M3 - Article

VL - 504

SP - 272

EP - 291

JO - Default journal

JF - Default journal

ER -