0000000000181528

AUTHOR

Stefania Aqué

showing 2 related works from this author

Computing the ℤ2-Cocharacter of 3 × 3 Matrices of Odd Degree

2013

Let F be a field of characteristic 0 and A = M 2, 1(F) the algebra of 3 × 3 matrices over F endowed with the only non trivial ℤ2-grading. Aver'yanov in [1] determined a set of generators for the T 2-ideal of graded identities of A. Here we study the identities in variables of homogeneous degree 1 via the representation theory of the symmetric group, and we determine the decomposition of the corresponding character into irreducibles.

Algebra and Number TheoryDegree (graph theory)Field (mathematics)Polynomial identityCocharacterCombinatoricsSet (abstract data type)GradingSettore MAT/02 - AlgebraCharacter (mathematics)Representation theory of the symmetric groupHomogeneousAlgebra over a fieldMathematicsCommunications in Algebra
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Cocharacters of Bilinear Mappings and Graded Matrices

2012

Let Mk(F) be the algebra of k ×k matrices over a field F of characteristic 0. If G is any group, we endow Mk(F) with the elementary grading induced by the k-tuple (1,...,1,g) where g ∈ G, g2 ≠ 1. Then the graded identities of Mk(F) depending only on variables of homogeneous degree g and g − 1 are obtained by a natural translation of the identities of bilinear mappings (see Bahturin and Drensky, Linear Algebra Appl 369:95–112, 2003). Here we study such identities by means of the representation theory of the symmetric group. We act with two copies of the symmetric group on a space of multilinear graded polynomials of homogeneous degree g and g − 1 and we find an explicit decomposition of the …

Multilinear mapDegree (graph theory)Group (mathematics)General MathematicsField (mathematics)Polynomial identitySpace (mathematics)CocharacterCombinatoricsGradingRepresentation theory of the symmetric groupSymmetric groupLinear algebraMathematicsAlgebras and Representation Theory
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