On finitely generated algebras with quadratic growth

Agata Smoktunowicz (Edinburgh)

Wednesday 9th April, 2008 16:00-17:00 214


A finitely generated K-algebra A has quadratic growth if for every finite-dimensional K-vector space V of A that contains 1 and generates A as a K-algebra, there exists positive constants C and D such that Dn^{2} < dim V^{n}< D n^{2} for all n>0. Notice that algebras with quadratic growth have Gelfand-Kirillov dimension two. Artin and Stafford showed that finitely generated graded domains with Gelfand-Kirillov dimension two have quadratic growth and showed that they are related to algebras of authomorphisms of some elliptic curves. In the talk we will mention some open results on algebras with quadratic growth and some open questions.

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