The Coxeter relations and KP map for non-commuting symbols

Abstract

We give an action of the symmetric group on non-commuting indeterminates in terms of series in the corresponding Mal'cev-Newmann division ring. The action is constructed from the non-Abelian Hirota-Miwa (discrete KP) system. The corresponding companion map, which gives generators of the action, is discussed in the generic case and the corresponding explicit formulas have been found in the periodic reduction. We discuss also briefly connection of the companion to the KP map with context-free languages.

arXiv comment13 pages, 3 figures

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Cited by in corpus (7)

• On non-abelian quadrirational Yang-Baxter maps
• Non-commutative bi-rational maps satisfying Zamolodchikov equation, and Desargues lattices
• Non-commutative Hermite--Padé approximation and integrability
• Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
• Discrete Lax pairs and hierarchies of integrable difference systems
• Hopf algebra structure of generalized quasi-symmetric functions in partially commutative variables
• Noncommutative solutions to Zamolodchikov's tetrahedron equation and matrix six-factorisation problems