6533b82ffe1ef96bd129531e

RESEARCH PRODUCT

Proper identities, Lie identities and exponential codimension growth

Mikhail ZaicevAntonino Giambruno

subject

Discrete mathematicsSequencePure mathematicsAlgebra and Number TheoryZero (complex analysis)CodimensionExponential functionPolynomial identitiesIntegerpolynomial identity codimensionsExponentCodimension growthExterior algebraAssociative propertyMathematics

description

Abstract The exponent exp ( A ) of a PI-algebra A in characteristic zero is an integer and measures the exponential rate of growth of the sequence of codimensions of A [A. Giambruno, M. Zaicev, On codimension growth of finitely generated associative algebras, Adv. Math. 140 (1998) 145–155; A. Giambruno, M. Zaicev, Exponential codimension growth of P.I. algebras: An exact estimate, Adv. Math. 142 (1999) 221–243]. In this paper we study the exponential rate of growth of the sequences of proper codimensions and Lie codimensions of an associative PI-algebra. We prove that the corresponding proper exponent exists for all PI-algebras, except for some algebras of exponent two strictly related to the Grassmann algebra. We also prove that the Lie exponent exists for any finitely generated PI-algebra. The value of both exponents is always equal to exp ( A ) or exp ( A ) − 1 .

yearjournalcountryeditionlanguage
2008-09-01
http://hdl.handle.net/10447/40060