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Representation Theory of Quantized Enveloping Algebras with Interpolating Real Structure
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Representation Theory of Quantized Enveloping Algebras with Interpolating Real Structure
Інший ID:
2010 Mathematics Subject Classification: 17B37; 20G42; 46L65
DOI: http://dx.doi.org/10.3842/SIGMA.2013.081
DOI: http://dx.doi.org/10.3842/SIGMA.2013.081
Посилання:
Representation Theory of Quantized Enveloping Algebras with Interpolating Real Structure / K. de Commer // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 33 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in
honor of Marc A. Rief fel. The full collection is available at http://www.emis.de/journals/SIGMA/Rieffel.html.
It is a pleasure to thank the following people for discussions on topics related to the subject
of this paper: J. Bichon, P. Bieliavsky, H.P. Jakobsen, E. Koelink, S. Kolb, U. Kr¨ahmer and
S. Neshveyev.
Дата:
2013
Переглядів:
577
Завантажень:
253
Анотація:
Let g be a compact simple Lie algebra. We modify the quantized enveloping ∗-algebra associated to 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.
