6533b838fe1ef96bd12a3ec6

RESEARCH PRODUCT

Algebras with intermediate growth of the codimensions

S. MishchenkoMikhail ZaicevAntonio Giambruno

subject

SequencePolynomialMathematics::Commutative Algebrapolynomia identityApplied MathematicsZero (complex analysis)Field (mathematics)CodimensionPolynomial identityCombinatoricsAlgebraBounded functionCodimension growthColength growthAlgebra over a fieldMathematicsReal number

description

AbstractLet F be a field of characteristic zero and let A be an F-algebra. The polynomial identities satisfied by A can be measured through the asymptotic behavior of the sequence of codimensions and the sequence of colengths of A. For finite dimensional algebras we show that the colength sequence of A is polynomially bounded and the codimension sequence cannot have intermediate growth. We then prove that for general nonassociative algebras intermediate growth of the codimensions is allowed. In fact, for any real number 0<β<1, we construct an algebra A whose sequence of codimensions grows like nnβ.

yearjournalcountryeditionlanguage
2006-09-01Advances in Applied Mathematics
https://doi.org/10.1016/j.aam.2005.02.005