6533b862fe1ef96bd12c7729
RESEARCH PRODUCT
Standard polynomials and matrices with superinvolutions
Antonio IoppoloFabrizio MartinoAntonio Giambrunosubject
Numerical AnalysisPolynomialAlgebra and Number TheoryDegree (graph theory)SuperinvolutionNumerical analysis010102 general mathematicsZero (complex analysis)Field (mathematics)010103 numerical & computational mathematicsPolynomial identity01 natural sciencesCombinatoricsMinimal degree; Polynomial identity; SuperinvolutionMinimal degreeTransposeDiscrete Mathematics and CombinatoricsIdeal (ring theory)Geometry and Topology0101 mathematicsNumerical AnalysiGeometry and topologyMathematicsdescription
Abstract Let M n ( F ) be the algebra of n × n matrices over a field F of characteristic zero. The superinvolutions ⁎ on M n ( 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 M n ( 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 M 2 ( F ) , we find generators of the ideal of ⁎-identities and we compute the corresponding sequences of cocharacters and codimensions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-09-01 |