Geometric algebra and quadrilateral lattices
Exactly Solvable and Integrable Systems
2008-01-04 v1
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.
Cite
@article{arxiv.0801.0512,
title = {Geometric algebra and quadrilateral lattices},
author = {Adam Doliwa},
journal= {arXiv preprint arXiv:0801.0512},
year = {2008}
}
Comments
12 pages, 5 figures