6533b86dfe1ef96bd12c9792
RESEARCH PRODUCT
Minimal varieties of algebras of exponential growth
Antonio GiambrunoMikhail Zaicevsubject
Discrete mathematicsMathematics(all)Pure mathematicsRank (linear algebra)General MathematicsMathematical analysisZero (complex analysis)Field (mathematics)CodimensionIntegerFree algebraExponentVariety (universal algebra)Mathematicsdescription
Abstract The exponent of a variety of algebras over a field of characteristic zero has been recently proved to be an integer. Through this scale we can now classify all minimal varieties of given exponent and of finite basic rank. As a consequence, we describe the corresponding T-ideals of the free algebra and we compute the asymptotics of the related codimension sequences, verifying in this setting some known conjectures. We also show that the number of these minimal varieties is finite for any given exponent. We finally point out some relations between the exponent of a variety and the Gelfand–Kirillov dimension of the corresponding relatively free algebras of finite rank.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-03-01 | Electronic Research Announcements of the American Mathematical Society |