Search results for "PI-ALGEBRAS"

showing 2 items of 2 documents

Varieties of almost polynomial growth: classifying their subvarieties

2007

Let G be the infinite dimensional Grassmann algebra over a field F of characteristic zero and UT2 the algebra of 2 x 2 upper triangular matrices over F. The relevance of these algebras in PI-theory relies on the fact that they generate the only two varieties of almost polynomial growth, i.e., they grow exponentially but any proper subvariety grows polynomially. In this paper we completely classify, up to PI-equivalence, the associative algebras A such that A is an element of Var(G) or A is an element of Var(UT2).

Discrete mathematicsPure mathematicsJordan algebraCODIMENSION GROWTHSubvarietyGeneral MathematicsTriangular matrixUniversal enveloping algebraIDENTITIESPI-ALGEBRASAlgebra representationDivision algebraCellular algebraComposition algebraT-IDEALSMathematics
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Codimensions of algebras and growth functions

2008

Abstract Let A be an algebra over a field F of characteristic zero and let c n ( A ) , n = 1 , 2 , … , be its sequence of codimensions. We prove that if c n ( A ) is exponentially bounded, its exponential growth can be any real number >1. This is achieved by constructing, for any real number α > 1 , an F-algebra A α such that lim n → ∞ c n ( A α ) n exists and equals α. The methods are based on the representation theory of the symmetric group and on properties of infinite Sturmian and periodic words.

Mathematics(all)SequenceGeneral MathematicsZero (complex analysis)polynomial identity codimension growthPI-algebrasCombinatoricsRepresentation theory of the symmetric groupExponential growthBounded functionCodimension growthAlgebra over a fieldMathematicsReal numberAdvances in Mathematics
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