Raimund Preusser (Nanjing University of Information Science and Technology)
Graded Bergman algebras
Abstract: This talk is about an ongoing research project with Roozbeh Hazrat and Huanhuan Li. Recall that for a (unital and associative) ring R, the V-monoid of R is the set of isomorphism classes of finitely generated projective left R-modules. It becomes an abelian monoid with direct sum. George Bergman has shown that any conical finitely generated abelian monoid with an order unit can be realised as the V-monoid of a hereditary algebra. We want to obtain a graded version of this result as follows. For an abelian group G, a G-monoid is an abelian monoid M together with an action of G on M via monoid homomorphisms. Our goal is to show that any conical finitely presented G-monoid with an order unit can be realised as the graded V-monoid of a G-graded algebra which is hereditary.