Geometric algebra and quadrilateral lattices

2008/01/03 by Adam Doliwa, Doliwa, Adam · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.48550/arxiv.0801.0512

12 pages, 5 figures

arxiv created 2008/01/03 · arxiv updated 2009/12/01

Abstract

Motivated by the fundamental results of the geometric algebra we study quadrilateral lattices in projective spaces over division rings. After giving the noncommutative discrete Darboux equations we discuss differences and similarities with the commutative case. Then we consider the fundamental transformation of such lattices in the vectorial setting and we show the corresponding permutability theorems. We discuss also the possibility of obtaining in a similar spirit a noncommutative version of the B-(Moutard) quadrilateral lattices.

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• Non-commutative lattice-modified Gel’fand–Dikii systems
• Hirota equation and the quantum plane

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