ON QUANTUM SPACES OF LIE-ALGEBRAS

The homogenization H(g) of the enveloping algebra of a finite dimensional Lie algebra g is an Artin-Schelter regular algebra. We characterize d-dimensional linear subspaces in the corresponding quantum space P(q)(g) as homogenizations of induced representations from codimension d Lie subalgebras. Furthermore we prove that the point variety has an embedded component iff there is a line, not contained in this point variety.