Title: Factoriality and class groups of cluster algebras Speaker: Daniel Smertnig (Dartmouth College and UniversitÃ¤t Graz)
Time: Friday, January 26, 2018 at 4:00 pm Place: MONT 313Abstract: Factorial domains (also called unique factorization domains) are classical objects of interest in commutative algebra. In this talk I present recent results on the factoriality of cluster algebras (and more generally, on their class groups). Using methods for Krull domains, we are able to characterize factoriality of acyclic cluster algebras explicitly in terms of their initial exchange matrix. As an easy corollary, this yields a classification of factoriality for cluster algebras of (extended) Dynkin type, significantly extending earlier results in this direction. This is joint work with Ana Garcia Elsener and Philipp Lampe.