Nil algebras, Lie algebras and wreath products with intermediate and oscillating growth

Greenfeld, Beeri1; Zelmanov, Efim2

2023-10-15

10.1016/j.aim.2023.109230

ADVANCES IN MATHEMATICS   Impact Factor & Quartile

0001-8708

1090-2082

We construct finitely generated nil algebras with prescribed growth rates. In particular, any increasing submultiplicative function is realized as the growth function of a nil algebra up to a polynomial error term and an arbitrarily slow distortion. We then move on to examples of nil algebras and domains with strongly oscillating growth functions and construct primitive algebras for which the Gel'fand-Kirillov dimension is strictly sub-additive with respect to tensor products, thus answering a question from [16,17].& COPY; 2023 Elsevier Inc. All rights reserved.

Nil algebras Nil Lie algebras Growth of algebras Matrix wreath products Gel'fand-Kirillov dimension Tensor products

SCI

English

Others

Mathematics

Mathematics

WOS:001061670600001

ACADEMIC PRESS INC ELSEVIER SCIENCE

MATHEMATICS

Web of Science

1.Univ Washington, Dept Math, Seattle, WA 98195 USA
2.Southern Univ Sci & Technol, SICM, Shenzhen 518055, Peoples R China

Greenfeld, Beeri,Zelmanov, Efim. Nil algebras, Lie algebras and wreath products with intermediate and oscillating growth[J]. ADVANCES IN MATHEMATICS,2023,431.

Greenfeld, Beeri,&Zelmanov, Efim.(2023).Nil algebras, Lie algebras and wreath products with intermediate and oscillating growth.ADVANCES IN MATHEMATICS,431.

Greenfeld, Beeri,et al."Nil algebras, Lie algebras and wreath products with intermediate and oscillating growth".ADVANCES IN MATHEMATICS 431(2023).