6533b853fe1ef96bd12ad6de
RESEARCH PRODUCT
Superinvolutions on upper-triangular matrix algebras
Fabrizio MartinoAntonio Ioppolosubject
PolynomialPure mathematicsAlgebra and Number Theory010102 general mathematicsPolynomial identity superinvolution upper-triangular matrices.Zero (complex analysis)Triangular matrixStructure (category theory)010103 numerical & computational mathematicsSingle class01 natural sciencesSuperalgebraSettore MAT/02 - Algebrapolynomial identity superinvolutions upper triangular matrices cocharacter0101 mathematicsAbelian groupAlgebraically closed fieldMathematicsdescription
Let UTn(F) be the algebra of n×n upper-triangular matrices over an algebraically closed field F of characteristic zero. In [18], the authors described all abelian G-gradings on UTn(F) by showing that any G-grading on this algebra is an elementary grading. In this paper, we shall consider the algebra UTn(F) endowed with an elementary Z2-grading. In this way, it has a structure of superalgebra and our goal is to completely describe the superinvolutions which can be defined on it. To this end, we shall prove that the superinvolutions and the graded involutions (i.e., involutions preserving the grading) on UTn(F) are strictly related through the so-called superautomorphisms of this algebra. We shall show that there exist two classes of inequivalent superinvolutions when n is even and a single class otherwise. Along the way, we shall give a complete description of the polynomial identities and the cocharacter sequences of UT2(F) and UT3(F) endowed with all possible superinvolutions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-08-01 |