# Michael Shapiro: Cluster algebras with Grassmann variables (joint with V. Ovsienko)

**Time: **
Mon 2019-05-27 11.00 - 12.00

**Location: **
Room 31, building 5, Kräftriket, Department of Mathematics, Stockholm University

**Participating: **
Michael Shapiro

**Abstract:** We develop a version of cluster algebra extending the ring of Laurent polynomials by adding Grassmann variables. These algebras can be described in terms of “extended quivers” which are oriented hypergraphs. We describe mutations of such objects and deﬁne a corresponding commutative superalgebra. Our construction includes the notion of weighted quivers that has already appeared in diﬀerent contexts. This project is a step towards understanding the notion of cluster superalgebra.