6533b7d9fe1ef96bd126cc3f
RESEARCH PRODUCT
Polynomial codimension growth of algebras with involutions and superinvolutions
Daniela La MattinaAntonio Ioppolosubject
Discrete mathematicsPure mathematicsAlgebra and Number TheorySubvarietySuperinvolution010102 general mathematicsSubalgebraGraded involution; Growth; Polynomial identity; SuperinvolutionTriangular matrix010103 numerical & computational mathematicsGroup algebraCodimensionPolynomial identity Graded involution Superinvolution GrowthGrowthPolynomial identity01 natural sciencesGraded involutionSettore MAT/02 - AlgebraBounded functionAssociative algebra0101 mathematicsFinite setMathematicsdescription
Abstract Let A be an associative algebra over a field F of characteristic zero endowed with a graded involution or a superinvolution ⁎ and let c n ⁎ ( A ) be its sequence of ⁎-codimensions. In [4] , [12] it was proved that if A is finite dimensional such sequence is polynomially bounded if and only if A generates a variety not containing a finite number of ⁎-algebras: the group algebra of Z 2 and a 4-dimensional subalgebra of the 4 × 4 upper triangular matrices with suitable graded involutions or superinvolutions. In this paper we focus our attention on such algebras since they are the only finite dimensional ⁎-algebras, up to T 2 ⁎ -equivalence, generating varieties of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety has polynomial growth. We classify the subvarieties of such varieties by giving a complete list of generating finite dimensional ⁎-algebras. Along the way we classify all minimal varieties of polynomial growth and surprisingly we show that their number is finite for any given growth. Finally we describe the ⁎-algebras whose ⁎-codimensions are bounded by a linear function.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-02-01 |