Factorizable Module Algebras.

The aim of this paper is to introduce and study a large class of g-module algebras that we call factorizable by generalizing the Gauss factorization of square or rectangular matrices. This class includes coordinate algebras of corresponding reductive groups G , their parabolic subgroups, basic affine spaces, and many others. It turns out that products of factorizable algebras are also factorizable and it is easy to create a factorizable algebra out of virtually any g-module algebra. We also have quantum versions of all these constructions in the category of U_q(g)-module algebras. Quite surprisingly, our quantum factorizable algebras are naturally acted on by the quantized enveloping algebra U_q(g*) of the dual Lie bialgebra g* of g⁠. [ABSTRACT FROM AUTHOR]