6533b870fe1ef96bd12cfcce

RESEARCH PRODUCT

Varieties of superalgebras of almost polynomial growth

Daniela La Mattina

subject

Discrete mathematicsSequencePolynomialPure mathematicsAlgebra and Number TheoryMathematics::Rings and AlgebrasTriangular matrixGrowthPolynomial identitySuperalgebrasuperalgebra growthBounded functionMathematics::Quantum AlgebraVarietyVariety (universal algebra)Mathematics::Representation TheoryExterior algebraCommutative propertyMathematics

description

Abstract Let V gr be a variety of superalgebras and let c n gr ( V gr ) , n = 1 , 2 , …  , be its sequence of graded codimensions. Such a sequence is polynomially bounded if and only if V gr does not contain a list of five superalgebras consisting of a commutative superalgebra, the infinite dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with trivial and natural Z 2 -gradings. In this paper we completely classify all subvarieties of the varieties generated by these five superalgebras, by giving a complete list of finite dimensional generating superalgebras.

yearjournalcountryeditionlanguage
2011-06-01Journal of Algebra
10.1016/j.jalgebra.2011.03.025http://dx.doi.org/10.1016/j.jalgebra.2011.03.025