**American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences**

2005; 277 pp; Hardcover

MSC: Primary 53; 81; Secondary 33

Print ISBN: 978-0-8218-4040-5

Product Code: TRANS2/216

Print ISBN: 978-0-8218-4040-5

Product Code: TRANS2/216

List Price: $126.00

Individual Member Price: $100.80

**Electronic ISBN: 978-1-4704-3427-4
Product Code: TRANS2/216.E**

List Price: $126.00

Individual Member Price: $100.80

# Quantum Algebras and Poisson Geometry in Mathematical Physics

Share this page *Edited by *
*M. V. Karasev*

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 .

#### Table of Contents

# Table of Contents

## Quantum Algebras and Poisson Geometry in Mathematical Physics

- Cover Cover11
- Title page iii4
- Copyright page iv5
- Contents v6
- Preface vii8
- Noncommutative algebras, nanostructures, and quantum dynamics generated by resonances 110
- Algebras with polynomial commutation relations for a quantum particle in electric and magnetic fields 1928
- Poisson structures and linear Euler systems over symplectic manifolds 137146
- Poisson equivalence over a symplectic leaf 241250
- Back Cover Back Cover1290

#### Readership

Graduate students and research mathematicians interested in mathematical physics.