Lectures on R-Algebras
R-algebras were introduced by S. Walcher in his 1985 dissertation;
they are characterized by the property that all solutions of the purely
quadratic Riccati differential equation in these algebras are rational. Since
power-associative algebras share this property, R-algebras may be viewed as a
generalization of power associative algebras.
This report is an extended version of a minicourse given in the algebra
seminar (I. Shestakov et al.) at IME, University of Sao Paulo, Brasil in the
fall of 2001. It contains in a unified treatment most of the material on
R-algebras which has been developed by S. Walcher, the author and some of their
students.
Kurt Meyberg < meyberg@ma.tum.de >