Non-commutative rational Yang-Baxter maps

2013/08/14 by Adam Doliwa · 2 citations
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.MP

paper · pdf · doi:10.1007/s11005-013-0669-7

published as Lett. Math. Phys. 104 (2014) 299-309 · 7 pages, 2 figures; Remark on p. 6 corrected (v2)

arxiv created 2013/08/14 · arxiv updated 2014/02/19

Abstract

Starting from multidimensional consistency of non-commutative lattice modified Gel'fand-Dikii systems we present the corresponding solutions of the functional (set-theoretic) Yang-Baxter equation, which are non-commutative versions of the maps arising from geometric crystals. Our approach works under additional condition of centrality of certain products of non-commuting variables. Then we apply such a restriction on the level of the Gel'fand-Dikii systems what allows to obtain non-autonomous (but with central non-autonomous factors) versions of the equations. In particular we recover known non-commutative version of Hirota's lattice sine-Gordon equation, and we present an integrable non-commutative and non-autonomous lattice modified Boussinesq equation.

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