Braided Symmetric Algebras of Simple $U_q(s{l}_2)$-Modules and Their Geometry

Abstract

In the present paper we prove decomposition formulae for the braided symmetric powers of simple modules over the quantized enveloping algebra $U_q(s{l}_2)$; natural quantum analogues of the classical symmetric powers of a module over a complex semisimple Lie algebra. We show that their point modules form natural non-commutative curves and surfaces and conjecture that braided symmetric algebras give rise to an interesting non-commutative geometry, which can be viewed as a flat deformation of the geometry associated to their classical limits.

19 pages,relationship to non--commutative geometry expanded

References in corpus (1)

• A quantum analogue of the first fundamental theorem of invariant theory