Noncommutative geometry and cayley-smooth orders - Le Bruyn, Lieven (Chapman & Hall/CRC, 2008)
The text covers the tale local structure of such orders and their central singularities and finite dimensional representations. It is based on a series of courses given since 1999 in the advanced master program on noncommutative geometry, organized by the Noncommutative Geometry (NOG) project, sponsored by the European Science Foundation. Background information on invariant theory, algebraic geometry, central simple algebras, and the representation theory of quivers is given, followed by chapters on the main results of Cayley-smooth orders, semisimple representations, nilpotent representations, noncommutative manifolds, and moduli spaces.