Geometric algebra and quadrilateral lattices

Details Geometric algebra and quadrilateral lattices Geometric algebra and quadrilateral lattices

2008-01-03

arxiv.org/abs/0801.0512v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, 5 figures

Scientific paper

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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