Search results for "Graded identities"

showing 2 items of 2 documents

Y-proper graded cocharacters and codimensions of upper triangular matrices of size 2, 3, 4

2012

Abstract Let F be a field of characteristic 0. We consider the upper triangular matrices with entries in F of size 2, 3 and 4 endowed with the grading induced by that of Vasilovsky. In this paper we give explicit computation for the multiplicities of the Y -proper graded cocharacters and codimensions of these algebras.

CombinatoricsSettore MAT/02 - AlgebraAlgebra and Number TheoryMathematics::Commutative AlgebraGraded identitiesComputationPolynomial identities graded identitiesTriangular matrixPolynomial identitiesMathematicsJournal of Algebra
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Gradings on the algebra of upper triangular matrices and their graded identities

2004

Abstract Let K be an infinite field and let UT n ( K ) denote the algebra of n × n upper triangular matrices over  K . We describe all elementary gradings on this algebra. Further we describe the generators of the ideals of graded polynomial identities of UT n ( K ) and we produce linear bases of the corresponding relatively free graded algebras. We prove that one can distinguish the elementary gradings by their graded identities. We describe bases of the graded polynomial identities in several “typical” cases. Although in these cases we consider elementary gradings by cyclic groups, the same methods serve for elementary gradings by any finite group.

Finite groupPolynomialPure mathematicsAlgebra and Number TheoryMathematics::Commutative AlgebraGraded identitiesMathematics::Rings and AlgebrasTriangular matrixGraded ringCyclic groupElementary gradingGraded Lie algebraUpper triangular matricesAlgebraDifferential graded algebraAlgebra over a fieldMathematics
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