Representation Theory of Quantized Enveloping Algebras with Interpolating Real Structure

Abstract

Let $\mathfrak{g}$ be a compact simple Lie algebra. We modify the quantized enveloping ${}^{\ast }$-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 ${}^{\ast }$-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.

Theorem 2.7 corrected

References in corpus (1)

• Hopf-Galois objects and cogroupoids

Cited by in corpus (5)

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• Ribbon braided module categories, quantum symmetric pairs and Knizhnik-Zamolodchikov equations
• I-factorial quantum torsors and Heisenberg algebras of quantized universal enveloping type
• Quantum flag manifolds as quotients of degenerate quantized universal enveloping algebras
• Invariant quantum measure on $q$-deformed twisted adjoint orbits