Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3238
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.
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
