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This article is cited in 5 scientific papers (total in 5 papers)
Representation Theory of Quantized Enveloping Algebras with Interpolating Real Structure
Kenny De Commer Department of Mathematics, University of Cergy-Pontoise,
UMR CNRS 8088, F-95000 Cergy-Pontoise, France
Abstract:
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.
Keywords:
compact quantum homogeneous spaces; quantized universal enveloping algebras; Hopf–Galois theory;
Verma modules.
Received: August 18, 2013; in final form December 18, 2013; Published online December 24, 2013
Citation:
Kenny De Commer, “Representation Theory of Quantized Enveloping Algebras with Interpolating Real Structure”, SIGMA, 9 (2013), 081, 20 pp.
Linking options:
https://www.mathnet.ru/eng/sigma864 https://www.mathnet.ru/eng/sigma/v9/p81
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