Representation Theory of Quantized Enveloping Algebras with Interpolating Real Structure

Symmetry Integrability and Geometry-Methods and Applications

article

Kenny De Commer¹ 

[1] Department of Mathematics, University of Cergy-Pontoise

关键词: compact quantum homogeneous spaces;    quantized universal enveloping algebras;    Hopf–Galois theory;    Verma modules;   

DOI  :  10.3842/SIGMA.2013.081

来源: National Academy of Science of Ukraine

【 摘 要 】

Let $\mathfrak{g}$ be a compact simple Lie algebra. We modify the quantized enveloping $^*$-algebra associated to $\mathfrak{g}$ by a real-valued character on the positive part of the root lattice. We study the ensuing Verma module theory, and the associated quotients of these modified quantized enveloping $^*$-algebras. Restricting to the locally finite part by means of a natural adjoint action, we obtain in particular examples of quantum homogeneous spaces in the operator algebraic setting.

【 授权许可】

Unknown