Gel'fand-Dikii Hamiltonian operator and the coadjoint representation of the Volterra group
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Publication:1150195
DOI10.1007/BF01078365zbMath0455.58012OpenAlexW1986443758MaRDI QIDQ1150195
Publication date: 1980
Published in: Functional Analysis and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01078365
Hamiltonian operatorLax equationcoadjoint representation of the Volterra groupGelfand-Dikii Lie algebra
Infinite-dimensional Lie (super)algebras (17B65) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Partial differential equations on manifolds; differential operators (58J99) Geometric quantization (53D50) Hyperbolic equations on manifolds (58J45)
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Cites Work
- Unnamed Item
- Lectures on geometric quantization
- On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
- Construction of unitary irreducible representations of Lie groups
- Associative differential operations
- Differential groups and formal Lie theory for an infinite number of parameters
- Differential groups of order two
- Subgroups of differential groups
- On Lie algebras of differential formal groups of Ritt