An introduction to associative geometry with applications to integrable systems
arXiv:1611.00644 · doi:10.1016/j.geomphys.2016.09.013
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.
Review article, 45 pages. To appear in Journal of Geometry and Physics