Construction of canonical coordinates for exponential Lie groups

DOI10.1090/S0002-9947-09-04936-8zbMath1187.22003OpenAlexW2094668009WikidataQ115289038 ScholiaQ115289038MaRDI QIDQ3648196

Didier Arnal, Béchir Dali, Bradley N. Currey

Publication date: 24 November 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-09-04936-8

zbMATH Keywords

coadjoint orbitexponential Lie groupsymplectic structure

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) Geometric quantization (53D50)

Related Items (10)

Infinitely small orbits in two-step nilpotent Lie algebras ⋮ Weak quadratic overgroups for a class of Lie groups ⋮ Canonical coordinates for a class of solvable groups ⋮ Coadjoint orbits in duals of Lie algebras with admissible ideals ⋮ Application of canonical coordinates for solving single-freedom constraint mechanical systems ⋮ Bandlimited spaces on some 2-step nilpotent Lie groups with one Parseval frame generator ⋮ Separation of coadjoint orbits of an exponential group by their convex envelops ⋮ The geometric nature of the Flaschka transformation ⋮ \(C^\ast\)-dynamical systems of solvable Lie groups ⋮ Orthonormal bases in the orbit of square-integrable representations of nilpotent Lie groups

Cites Work

• Unnamed Item
• Représentations \({}^*\) des groupes exponentiels. \((^*\)- representations of exponential groups)
• Explicit orbital parameters and the Plancherel measure for exponential Lie groups
• On the symplectic structure of coadjoint orbits of (solvable) Lie groups and applications. I
• The Structure of the Space of Coadjoint Orbits of an Exponential Solvable Lie Group
• Geometric Quantization and The Universal Enveloping Algebra of a Nilpotent Lie Group
• Unitary representations of solvable Lie groups
• Polarized deformations of algebras on the coadjoint orbits of exponential groups

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