0000000000497045

AUTHOR

Eli Aljadeff

showing 3 related works from this author

Multialternating graded polynomials and growth of polynomial identities

2012

Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by mean of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non vanishing on A. As a consequence we compute the exponential rate of growth of the sequence of graded codimensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. In particular we show it is an integer. The result was proviously known in case G is abelian.

Discrete mathematicsPure mathematicsHilbert series and Hilbert polynomialMathematics::Commutative AlgebraApplied MathematicsGeneral MathematicsMathematics::Rings and AlgebrasGraded ringMathematics - Rings and AlgebrasGraded Lie algebramultialternating polynomialFiltered algebrasymbols.namesakeReciprocal polynomialRings and Algebras (math.RA)Differential graded algebraFactorization of polynomialssymbolsFOS: MathematicsElementary symmetric polynomial16R50 16P90 16R10 16W50Mathematics
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Polynomial identities with involution, superinvolutions and the Grassmann envelope

2017

Let A be an algebra with involution ∗ over a field of characteristic zero. We prove that in case A satisfies a non-trivial ∗-identity, then A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution. As a consequence we give a positive answer to the Specht problem for algebras with involution, i.e., any T-ideal of identities of an algebra with involution is finitely generated as a T-ideal.

Discrete mathematicsInvolution (mathematics)Pure mathematicsInvolutionGrassmann algebraSuperinvolutionGeneral MathematicsApplied MathematicsPolynomial identityGrassmann numberSuperinvolutionMathematics (all)Exterior algebraMathematics
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Graded polynomial identities and exponential growth

2009

Let $A$ be a finite dimensional algebra over a field of characteristic zero graded by a finite abelian group $G$. Here we study a growth function related to the graded polynomial identities satisfied by $A$ by computing the exponential rate of growth of the sequence of graded codimensions of $A$. We prove that the $G$-exponent of $A$ exists and is an integer related in an explicit way to the dimension of a suitable semisimple subalgebra of $A$.

Pure mathematicsPolynomialMathematics::Commutative AlgebraApplied MathematicsGeneral MathematicsMathematics::Rings and AlgebrasMathematics - Rings and AlgebrasSettore MAT/02 - Algebra16R10 16W50 16P90Exponential growthRings and Algebras (math.RA)FOS: Mathematicsgraded algebra polynomial identity growth codimensionsMathematics
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