6533b861fe1ef96bd12c4538

RESEARCH PRODUCT

PI-algebras with slow codimension growth

D. La MattinaAntonio Giambruno

subject

Discrete mathematicsLinear function (calculus)SequenceAlgebra and Number Theorypolynomial identity T-ideal codimensionsZero (complex analysis)Field (mathematics)CodimensionPolynomial identityT-idealCodimensionsCombinatoricsSettore MAT/02 - AlgebraBounded functionPiAlgebra over a fieldMathematics

description

Let $c_n(A),\ n=1,2,\ldots,$ be the sequence of codimensions of an algebra $A$ over a field $F$ of characteristic zero. We classify the algebras $A$ (up to PI-equivalence) in case this sequence is bounded by a linear function. We also show that this property is closely related to the following: if $l_n(A), \ n=1,2,\ldots, $ denotes the sequence of colengths of $A$, counting the number of $S_n$-irreducibles appearing in the $n$-th cocharacter of $A$, then $\lim_{n\to \infty} l_n(A)$ exists and is bounded by $2$.

yearjournalcountryeditionlanguage
2005-02-01Journal of Algebra
10.1016/j.jalgebra.2004.09.003http://dx.doi.org/10.1016/j.jalgebra.2004.09.003