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arXiv · 1908.00565

On the $3D$ consistency of a Grassmann extended lattice Boussinesq system

Sotiris Konstantinou-Rizos
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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 P$\Delta$Es, based on the ideas presented in \cite{Sokor-Kouloukas}. 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.

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Sotiris Konstantinou-Rizos. 2019-08-01. On the $3D$ consistency of a Grassmann extended lattice Boussinesq system. https://doi.org/10.1016/j.nuclphysb.2019.114878

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