https://doi.org/10.1016/j.nuclphysb.2019.114878

Abstract

In this paper, we formulate a “Grassmann extension” scheme for constructing noncommutative (Grassmann) extensions of Yang-Baxter maps together with their associated systems of PΔEs, based on the ideas presented in [15]. Using this scheme, we first construct a Grassmann extension of a Yang-Baxter map which constitutes a lift of a lattice Boussinesq system. The Grassmann-extended Yang-Baxter map can be squeezed down to a novel, integrable, Grassmann lattice Boussinesq system, and we derive its 3D-consistent limit. We show that some systems retain their 3D-consistency property in their Grassmann extension.