AbstractWe show that over every countable algebraically closed field $\mathbb{K}$ there exists a finitely generated $\mathbb{K}$-algebra that is Jacobson radical, infinite-dimensional, generated by two elements, graded and has quadratic growth. We also propose a way of constructing examples of algebras with quadratic growth that satisfy special types of relations.</jats:p

Smoktunowicz, Agata

Young, Alexander A.

Crossref

Edinburgh Research Explorer

English

Agata Smoktunowicz, Images of Golod-Shafarevich algebras with small growth,

An in dimensional algebra with  Gelfand-Kirillov algebra,

Ane algebras of Gelfand-Kirillov dimension one are PI,

Branch rings, thinned rings, tree enveloping rings,

Growth of algebras and GelfandKirillov dimension, Revised edition.

Jacobson radical algebras with Gelfand-Kirillov dimension two over countable

Jacobson radical non-nil algebras of Gelfand-Kirillov dimension 2, to appear in

Nil algebras with restricted growth, to appear in Proc.Edin.Math.Soc.Jacobson radical algebras with quadratic growth 17

Uzi Primitive algebras with arbitrary Gelfand-Kirillov dimension.

JACOBSON RADICAL ALGEBRAS WITH QUADRATIC GROWTH