Search results for "graded polynomial"

showing 3 items of 3 documents

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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Polynomial identities on superalgebras: Classifying linear growth

2006

Abstract We classify, up to PI-equivalence, the superalgebras over a field of characteristic zero whose sequence of codimensions is linearly bounded. As a consequence we determine the linear functions describing the graded codimensions of a superalgebra.

Discrete mathematicsPolynomialPure mathematicsSequenceAlgebra and Number TheoryMathematics::Commutative AlgebraMathematics::Rings and AlgebrasZero (complex analysis)Field (mathematics)graded polynomial identity T_2-ideal graded codimensionsSuperalgebraSettore MAT/02 - AlgebraMathematics::Quantum AlgebraBounded functionMathematics::Representation TheoryLinear growthMathematicsJournal of Pure and Applied Algebra
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Cocharacters of group graded algebras and multiplicities bounded by one

2017

Let G be a finite group and A a G-graded algebra over a field F of characteristic zero. We characterize the (Formula presented.)-ideals (Formula presented.) of graded identities of A such that the multiplicities (Formula presented.) in the graded cocharacter of A are bounded by one. We do so by exhibiting a set of identities of the (Formula presented.)-ideal. As a consequence we characterize the varieties of G-graded algebras whose lattice of subvarieties is distributive.

Pure mathematics010103 numerical & computational mathematics01 natural sciencesGraded Lie algebraFiltered algebrasymbols.namesakeDifferential graded algebra0101 mathematicsAlgebra over a fieldMathematicsDiscrete mathematicsHilbert series and Hilbert polynomialFinite groupAlgebra and Number TheoryMathematics::Commutative AlgebraMathematics::Rings and Algebras010102 general mathematicsGraded ringPolynomial identitycocharactergraded polynomialSettore MAT/02 - AlgebraBounded functiongraded algebrasymbolsANÉIS E ÁLGEBRAS ASSOCIATIVOS
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