An Introduction to Supersymmetric Cluster Algebras

Abstract

In this paper we propose the notion of cluster superalgebras which is a supersymmetric version of the classical cluster algebras introduced by Fomin and Zelevinsky. We show that the symplectic-orthogonal supergroup $SpO(2|1)$ admits a cluster superalgebra structure and as a consequence of this, we deduce that the supercommutative superalgebra generated by all the entries of a superfrieze is a subalgebra of a cluster superalgebra. We also show that the coordinate superalgebra of the super Grassmannian $G(2|0;4|1)$ of chiral conformal superspace (that is, $(2|0)$ planes inside the superspace ${\mathbb{C}}^{4|1}$) is a quotient of a cluster superalgebra.

To appear in The Electronic Journal of Combinatorics

Cited by in corpus (2)

• On super Plücker embedding and cluster algebras
• Cluster algebras with Grassmann variables