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Superinvolutions on upper-triangular matrix algebras

2018

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 …

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 fieldMathematics
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