An introduction to associative geometry with applications to integrable systems
Abstract
The aim of these notes is to provide a reasonably short and ;hands-on; introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory associative geometry. We argue that this formalism sheds a new light on some classic solution methods in the theory of finite-dimensional integrable dynamical systems.
- Publication:
-
Journal of Geometry and Physics
- Pub Date:
- August 2017
- DOI:
- 10.1016/j.geomphys.2016.09.013
- arXiv:
- arXiv:1611.00644
- Bibcode:
- 2017JGP...118..202T
- Keywords:
-
- Mathematical Physics;
- 70H06 (Primary);
- 14A22;
- 16G20 (Secondary)
- E-Print:
- Review article, 45 pages. To appear in Journal of Geometry and Physics