Search results for "Graded codimension"

showing 2 items of 2 documents

Graded algebras with polynomial growth of their codimensions

2015

Abstract Let A be an algebra over a field of characteristic 0 and assume A is graded by a finite group G . We study combinatorial and asymptotic properties of the G -graded polynomial identities of A provided A is of polynomial growth of the sequence of its graded codimensions. Roughly speaking this means that the ideal of graded identities is “very large”. We relate the polynomial growth of the codimensions to the module structure of the multilinear elements in the relatively free G -graded algebra in the variety generated by A . We describe the irreducible modules that can appear in the decomposition, we show that their multiplicities are eventually constant depending on the shape obtaine…

Discrete mathematicsHilbert series and Hilbert polynomialPure mathematicsPolynomialMultilinear mapAlgebra and Number TheoryMathematics::Commutative AlgebraGraded ringGraded codimensionsymbols.namesakeSettore MAT/02 - AlgebraPI exponentDifferential graded algebrasymbolsMultipartitionGraded identitieVariety (universal algebra)Algebra over a fieldCodimension growthMathematics
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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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