Cluster algebras with Grassmann variables

Understand

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.