Quantization of semisimple real Lie groups

Kenny De Commer

Archivum Mathematicum (2024)

  • Volume: 060, Issue: 5, page 285-310
  • ISSN: 0044-8753

Abstract

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We provide a novel construction of quantized universal enveloping * -algebras of real semisimple Lie algebras, based on Letzter’s theory of quantum symmetric pairs. We show that these structures can be ‘integrated’, leading to a quantization of the group C * -algebra of an arbitrary semisimple algebraic real Lie group.

How to cite

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De Commer, Kenny. "Quantization of semisimple real Lie groups." Archivum Mathematicum 060.5 (2024): 285-310. <http://eudml.org/doc/299661>.

@article{DeCommer2024,
abstract = {We provide a novel construction of quantized universal enveloping $*$-algebras of real semisimple Lie algebras, based on Letzter’s theory of quantum symmetric pairs. We show that these structures can be ‘integrated’, leading to a quantization of the group C$^*$-algebra of an arbitrary semisimple algebraic real Lie group.},
author = {De Commer, Kenny},
journal = {Archivum Mathematicum},
keywords = {quantum groups; real forms; quantized enveloping algebras; Harish-Chandra modules},
language = {eng},
number = {5},
pages = {285-310},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Quantization of semisimple real Lie groups},
url = {http://eudml.org/doc/299661},
volume = {060},
year = {2024},
}

TY - JOUR
AU - De Commer, Kenny
TI - Quantization of semisimple real Lie groups
JO - Archivum Mathematicum
PY - 2024
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 060
IS - 5
SP - 285
EP - 310
AB - We provide a novel construction of quantized universal enveloping $*$-algebras of real semisimple Lie algebras, based on Letzter’s theory of quantum symmetric pairs. We show that these structures can be ‘integrated’, leading to a quantization of the group C$^*$-algebra of an arbitrary semisimple algebraic real Lie group.
LA - eng
KW - quantum groups; real forms; quantized enveloping algebras; Harish-Chandra modules
UR - http://eudml.org/doc/299661
ER -

References

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