An introduction to cluster superalgebras

Monday, August 21, 2017 - 11:15am - 12:00pm
Lind 305
Ashish Srivastava (Saint Louis University)
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 superalgebras SpO(21) and SpO(22) admit cluster superalgebra structures and as a consequence of this, we also deduce that the supercommutative superalgebra generated by all the entries of a superfrieze is a cluster superalgebra. We also discuss some basic properties of cluster superalgebras and observe their similarities and differences with the classical set up. We will also discuss how Sage can help in further developing this notion.
MSC Code: 
17A70, 13F60