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.

13 pages, 3 figures

References in corpus (3)

• Quantum groups, Yang-Baxter maps and quasi-determinants
• Quantization of three-wave equations
• Non-commutative double-sided continued fractions

Cited by in corpus (6)

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• Non-commutative bi-rational maps satisfying Zamolodchikov equation, and Desargues lattices
• Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
• Non-commutative Hermite--Padé approximation and integrability
• Discrete Lax pairs and hierarchies of integrable difference systems
• Noncommutative solutions to Zamolodchikov's tetrahedron equation and matrix six-factorisation problems