A deformation approach of the Kirillov map for exponential groups

DOI10.1515/APAM.2010.038zbMath1229.22009OpenAlexW2020580417MaRDI QIDQ3093138

Ali Baklouti, Dominique Manchon, Sami Dhieb

Publication date: 12 October 2011

Published in: Advances in Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/apam.2010.038

zbMATH Keywords

Lie groupsdeformationsLie algebrassolvable Lie groupsquantizationsexponential Lie groupsKirillov map

Mathematics Subject Classification ID

Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Nilpotent and solvable Lie groups (22E25) Deformation quantization, star products (53D55)

Cites Work

• Coadjoint orbits and characteristic varieties.
• The structure of algebras of operator fields
• Représentations \({}^*\) des groupes exponentiels. \((^*\)- representations of exponential groups)
• On the symplectic structure of coadjoint orbits of (solvable) Lie groups and applications. I
• Lie groupoid \(C^*\)-algebras and Weyl quantization
• Polarization and unitary representations of solvable Lie groups. Appendix by Calvin C. Moore
• Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures

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