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Advances in the Mathematical Sciences
Quantum Algebras and Poisson Geometry in Mathematical Physics
Edited by: M. V. Karasev, Moscow Institute of Electronics and Mathematics, Russia
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American Mathematical Society Translations--Series 2
Advances in the Mathematical Sciences
2005; 277 pp; hardcover
Volume: 216
ISBN-10: 0-8218-4040-1
ISBN-13: 978-0-8218-4040-5
List Price: US$120
Member Price: US$96
Order Code: TRANS2/216
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This collection presents new and interesting applications of Poisson geometry to some fundamental well-known problems in mathematical physics. In addition to advanced Poisson geometry, the methods used by the authors include unexpected algebras with non-Lie commutation relations, nontrivial (quantum) Kählerian structures of hypergeometric type, dynamical systems theory, semiclassical asymptotics, and more.

The volume is suitable for graduate students and researchers interested in mathematical physics.

Other AMS publications by M. Karasev include Nonlinear Poisson Brackets. Geometry and Quantization, Coherent Transform, Quantization, and Poisson Geometry, and Asymptotic Methods for Wave and Quantum Problems.

Readership

Graduate students and research mathematicians interested in mathematical physics.

Table of Contents

  • M. Karasev -- Noncommutative algebras, nanostructures, and quantum dynamics generated by resonances
  • M. Karasev and E. Novikova -- Algebras with polynomial commutation relations for a quantum particle in electric and magnetic fields
  • Y. Vorobjev -- Poisson structures and linear Euler systems over symplectic manifolds
  • Y. Vorobjev -- Poisson equivalence over a symplectic leaf
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