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RESEARCH PRODUCT
Codimensions of algebras and growth functions
S. MishchenkoAntonio GiambrunoMikhail Zaicevsubject
Mathematics(all)SequenceGeneral MathematicsZero (complex analysis)polynomial identity codimension growthPI-algebrasCombinatoricsRepresentation theory of the symmetric groupExponential growthBounded functionCodimension growthAlgebra over a fieldMathematicsReal numberdescription
Abstract Let A be an algebra over a field F of characteristic zero and let c n ( A ) , n = 1 , 2 , … , be its sequence of codimensions. We prove that if c n ( A ) is exponentially bounded, its exponential growth can be any real number >1. This is achieved by constructing, for any real number α > 1 , an F-algebra A α such that lim n → ∞ c n ( A α ) n exists and equals α. The methods are based on the representation theory of the symmetric group and on properties of infinite Sturmian and periodic words.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-02-01 | Advances in Mathematics |