6533b822fe1ef96bd127cd16
RESEARCH PRODUCT
Polynomial growth and star-varieties
Fabrizio MartinoDaniela La Mattinasubject
Involution (mathematics)Algebra and Number TheorySubvariety010102 general mathematicsSubalgebraStar-codimensionTriangular matrixStar-polynomial identitie010103 numerical & computational mathematicsGrowth01 natural sciencesCombinatoricsSettore MAT/02 - AlgebraExponential growthBounded function0101 mathematicsCommutative algebraAssociative propertyMathematicsdescription
Abstract Let V be a variety of associative algebras with involution over a field F of characteristic zero and let c n ⁎ ( V ) , n = 1 , 2 , … , be its ⁎-codimension sequence. Such a sequence is polynomially bounded if and only if V does not contain the commutative algebra F ⊕ F , endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4 × 4 upper triangular matrices. Such algebras generate the only varieties of ⁎-algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all subvarieties of the ⁎-varieties of almost polynomial growth by giving a complete list of finite dimensional ⁎-algebras generating them.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-01-01 |