A step towards cluster superalgebras

Understand

We introduce a class of commutative superalgebras generalizing cluster algebras.

• A cluster superalgebra is defined by a hypergraph called an "extended quiver", and transformations called mutations.
• We prove the super analog of the "Laurent phenomenon", i.e., that all elements of a given cluster superalgebra are Laurent polynomials in the initial variables, and find an invariant presymplectic form.
• Examples of cluster superalgebras are provided by superanalogs of Coxeter's frieze patterns.