Search results for " Cocharacter"

showing 6 items of 6 documents

Computing with Rational Symmetric Functions and Applications to Invariant Theory and PI-algebras

2012

The research of the first named author was partially supported by INdAM. The research of the second, third, and fourth named authors was partially supported by Grant for Bilateral Scientific Cooperation between Bulgaria and Ukraine. The research of the fifth named author was partially supported by NSF Grant DMS-1016086.

Classical Invariant Theory05A15 05E05 05E10 13A50 15A72 16R10 16R30 20G05MacMahon Partition AnalysisHilbert SeriesRational symmetric functions classical invariant theory algebras with polynomial identity cocharacter sequenceMathematics - Rings and AlgebrasCommutative Algebra (math.AC)Mathematics - Commutative AlgebraRational Symmetric FunctionsAlgebras with Polynomial IdentitySettore MAT/02 - AlgebraRings and Algebras (math.RA)Noncommutative Invariant TheoryFOS: MathematicsCocharacter SequenceMathematics - CombinatoricsCombinatorics (math.CO)
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Ordinary and graded cocharacter of the Jordan algebra of 2x2 upper triangular matrices

2014

Abstract Let F be a field of characteristic zero and U J 2 ( F ) be the Jordan algebra of 2 × 2 upper triangular matrices over F . In this paper we give a complete description of the space of multilinear graded and ordinary identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . For every Z 2 -grading of U J 2 ( F ) we compute the multiplicities in the graded cocharacter sequence and furthermore we compute the ordinary cocharacter.

Discrete mathematicsNumerical AnalysisSequenceMultilinear mapPure mathematicsAlgebra and Number TheoryJordan algebraZero (complex analysis)Triangular matrixField (mathematics)Space (mathematics)Representation theoryJordan algebras Polynomial identities Basis of identities Cocharacter Gradings Graded polynomial identitiesSettore MAT/02 - AlgebraDiscrete Mathematics and CombinatoricsGeometry and TopologyMathematics
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Group graded algebras and multiplicities bounded by a constant

2013

AbstractLet G be a finite group and A a G-graded algebra over a field of characteristic zero. When A is a PI-algebra, the graded codimensions of A are exponentially bounded and one can study the corresponding graded cocharacters via the representation theory of products of symmetric groups. Here we characterize in two different ways when the corresponding multiplicities are bounded by a constant.

Discrete mathematicsPure mathematicsFinite groupAlgebra and Number TheoryMathematics::Commutative AlgebraGroup (mathematics)Zero (complex analysis)Polynomial identities Graded algebras cocharactersRepresentation theorySettore MAT/02 - AlgebraSymmetric groupBounded functionAlgebra over a fieldConstant (mathematics)MathematicsJournal of Pure and Applied Algebra
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Classifying Algebras with Graded Involutions or Superinvolutions with Multiplicities of their Cocharacter Bounded by One

2020

Let A be superalgebra over a field of characteristic zero and let ∗ be either a graded involution or a superinvolution defined on A. In this paper we characterize the ∗-algebras whose ∗-cocharacter has multiplicities bounded by one, showing a set of ∗-polynomial identities satisfied by such algebras.

Involution (mathematics)Pure mathematicsGeneral Mathematics010102 general mathematics0211 other engineering and technologies021107 urban & regional planning02 engineering and technology01 natural sciencesSuperalgebraSettore MAT/02 - AlgebraSuperinvolutionPolynomial identity cocharacter super involution graded involutionBounded function0101 mathematicsMathematics
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Gradings on the algebra of upper triangular matrices of size three

2013

Abstract Let UT 3 ( F ) be the algebra of 3 × 3 upper triangular matrices over a field F . On UT 3 ( F ) , up to isomorphism, there are at most five non-trivial elementary gradings and we study the graded polynomial identities for such gradings. In case F is of characteristic zero we give a complete description of the space of multilinear graded identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . We finally compute the multiplicities in the graded cocharacter sequence for every elementary G -grading on UT 3 ( F ) .

Numerical AnalysisMultilinear mapPolynomialAlgebra and Number TheoryMathematics::Commutative AlgebraMathematics::Rings and AlgebrasZero (complex analysis)Triangular matrixField (mathematics)Representation theorypolynomial identity G-graded algebras cocharacters graded ideals of identitiesCombinatoricsAlgebraSettore MAT/02 - AlgebraDifferential graded algebraDiscrete Mathematics and CombinatoricsGeometry and TopologyIsomorphismComputer Science::Information TheoryMathematics
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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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