On quantum spaces of Lie algebras

Abstract:

The homogenization $H(\mathfrak {g})$ of the enveloping algebra of a finite dimensional Lie algebra $\mathfrak {g}$ is an Artin-Schelter regular algebra. We characterize $d$-dimensional linear subspaces in the corresponding quantum space ${\mathbb {P}_q}(\mathfrak {g})$ 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.