Turkish Journal of Mathematics
Abstract
Let $F$ be an algebraically closed field of characteristic zero. In this paper we deal with matrix superalgebras (i.e. algebras graded by $\mathbb{Z}_2$, the cyclic group of order $2$) endowed with a pseudoinvolution. The first goal is to present the classification of the pseudoinvolutions that it is possible to define, up to equivalence, in the full matrix algebra $M_n(F)$ of $n \times n$ matrices and on its subalgebra $UT_n(F)$ of upper-triangular matrices. Along the way we shall give the generators of the $T$-ideal of identities for the algebras $M_2(F)$, $UT_2(F)$ and $UT_3(F)$, endowed with all possible inequivalent pseudoinvolutions.
DOI
10.55730/1300-0098.3238
Keywords
Polynomial identities, matrix algebras, superalgebras, pseudoinvolutions
First Page
1871
Last Page
1885
Recommended Citation
IOPPOLO, ANTONIO
(2022)
"Polynomial identities in matrix algebras with pseudoinvolution,"
Turkish Journal of Mathematics: Vol. 46:
No.
5, Article 17.
https://doi.org/10.55730/1300-0098.3238
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss5/17
