Quantum groups and double quiver algebras

Abstract

For a finite dimensional semisimple Lie algebra $\mathfrak{g}$ and a root $q$ of unity in a field $k,$ we associate to these data a double quiver $\bar{\mathcal{Q}}.$ It is shown that a restricted version of the quantized enveloping algebras $U_q(\mathfrak{g})$ is a quotient of the double quiver algebra $k\bar{\mathcal{Q}}.$

15 pages