Search results for " polynomial identity"

showing 5 items of 15 documents

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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Varieties of Algebras with Superinvolution of Almost Polynomial Growth

2015

Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let $c_{n}^{\ast }(A)$ be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.

SequencePolynomialSuperinvolutionGeneral Mathematics010102 general mathematicsGrowth; Polynomial identity; SuperinvolutionZero (complex analysis)Field (mathematics)010103 numerical & computational mathematicsGrowthPolynomial identity01 natural sciencesExponential functionCombinatoricsSettore MAT/02 - AlgebraBounded functionAssociative algebraMathematics (all)0101 mathematicsVariety (universal algebra)Mathematics
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MR2966998 Aljadeff, Eli; Kanel-Belov, Alexei Hilbert series of PI relatively free G-graded algebras are rational functions. Bull. Lond. Math. Soc. 44…

2013

Settore MAT/02 - AlgebraGraded Algebra polynomial identity
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MR3038546, Brešar, Matej; Klep, Igor A local-global principle for linear dependence of noncommutative polynomials. Israel J. Math. 193 (2013), no. 1,…

2014

Let F be a eld of characteristic zero and FhXi the free associative algebra on X = fX1;X2; : : : g over F; i.e., the algebra of polynomials in the non-commuting variables Xi 2 X. A set of polynomials in FhXi is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. In [Integral Equations Operator Theory 46 (2003), no. 4, 399{454; MR1997979 (2004f:90102)], J. F. Camino et al., in the setting of free analysis, motivated by systems engineering, proved that a nite locally linearly dependent set of polynomials is linearly dependent. In this paper the authors give an alternative algebraic proof of this result based on the theory of polynomial i…

Settore MAT/02 - AlgebraLocally linearly dependent polynomial identity
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On the growth of the identities of algebras

2006

growth polynomial identity
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