### 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 originale | English |
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pagine (da-a) | 272-291 |

Numero di pagine | 20 |

Rivista | Linear Algebra and Its Applications |

Volume | 504 |

Stato di pubblicazione | Published - 2016 |

### All Science Journal Classification (ASJC) codes

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

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## Cita questo

Giambruno, A., Martino, F., Martino, F., & Ioppolo, A. (2016). Standard polynomials and matrices with superinvolutions.

*Linear Algebra and Its Applications*,*504*, 272-291.