An introduction to associative geometry with applications to integrable systems

Understand

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.