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Quantization, Poisson Brackets and Beyond
 
Edited by: Theodore Voronov University of Manchester Institute of Science and Technology (UMIST), Manchester, England
Quantization, Poisson Brackets and Beyond
Softcover ISBN:  978-0-8218-3201-1
Product Code:  CONM/315
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7905-4
Product Code:  CONM/315.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-3201-1
eBook: ISBN:  978-0-8218-7905-4
Product Code:  CONM/315.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Quantization, Poisson Brackets and Beyond
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Quantization, Poisson Brackets and Beyond
Edited by: Theodore Voronov University of Manchester Institute of Science and Technology (UMIST), Manchester, England
Softcover ISBN:  978-0-8218-3201-1
Product Code:  CONM/315
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7905-4
Product Code:  CONM/315.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-3201-1
eBook ISBN:  978-0-8218-7905-4
Product Code:  CONM/315.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 3152002; 280 pp
    MSC: Primary 53; 46; 17; 18; 58

    The papers in this volume are based on talks given at the 2001 Manchester Meeting of the London Mathematical Society, which was followed by an international workshop on “Quantization, Deformations, and New Homological and Categorical Methods in Mathematical Physics”.

    The focus is on the topics suggested by the title: Quantization in its various aspects, Poisson brackets and generalizations, and structures “beyond”, including symplectic supermanifolds, operads, Lie groupoids and Lie (bi)algebroids and algebras with \(n\)-ary operations. This book offers accounts of new results as well as accessible expositions useful to a broad reading audience of researchers in differential geometry, algebraic topology and mathematical physics.

    Readership

    Graduate students and research mathematicians interested in mathematical physics, differential geometry, and algebraic topology.

  • Table of Contents
     
     
    • Articles
    • Boris Fedosov — Deformation quantization: pro and contra [ MR 1958826 ]
    • N. P. Landsman — Quantization as a functor [ MR 1958827 ]
    • Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki and Akira Yoshioka — Star exponential functions for quadratic forms and polar elements [ MR 1958828 ]
    • John Rawnsley — On traces for differential star products on symplectic manifolds [ MR 1958829 ]
    • Joseph Donin — Quantum $G$-manifolds [ MR 1958830 ]
    • J. Donin and A. Mudrov — ${\scr U}_q({\rm sl}(n))$-covariant quantization of symmetric coadjoint orbits via reflection equation algebra [ MR 1958831 ]
    • Olga Radko — Toward a classification of Poisson structures on surfaces [ MR 1958832 ]
    • J. D. S. Jones — Lectures on operads [ MR 1958833 ]
    • Theodore Voronov — Graded manifolds and Drinfeld doubles for Lie bialgebroids [ MR 1958834 ]
    • Dmitry Roytenberg — On the structure of graded symplectic supermanifolds and Courant algebroids [ MR 1958835 ]
    • K. C. H. Mackenzie — On certain canonical diffeomorphisms in symplectic and Poisson geometry [ MR 1958836 ]
    • Hovhannes M. Khudaverdian — Laplacians in odd symplectic geometry [ MR 1958837 ]
    • Y. Kosmann-Schwarzbach and K. C. H. Mackenzie — Differential operators and actions of Lie algebroids [ MR 1958838 ]
    • Long-guang He, Zhang-Ju Liu and De-Shou Zhong — Poisson actions and Lie bialgebroid morphisms [ MR 1958839 ]
    • A. S. Dzhumadil′daev — Identities and derivations for Jacobian algebras [ MR 1958840 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3152002; 280 pp
MSC: Primary 53; 46; 17; 18; 58

The papers in this volume are based on talks given at the 2001 Manchester Meeting of the London Mathematical Society, which was followed by an international workshop on “Quantization, Deformations, and New Homological and Categorical Methods in Mathematical Physics”.

The focus is on the topics suggested by the title: Quantization in its various aspects, Poisson brackets and generalizations, and structures “beyond”, including symplectic supermanifolds, operads, Lie groupoids and Lie (bi)algebroids and algebras with \(n\)-ary operations. This book offers accounts of new results as well as accessible expositions useful to a broad reading audience of researchers in differential geometry, algebraic topology and mathematical physics.

Readership

Graduate students and research mathematicians interested in mathematical physics, differential geometry, and algebraic topology.

  • Articles
  • Boris Fedosov — Deformation quantization: pro and contra [ MR 1958826 ]
  • N. P. Landsman — Quantization as a functor [ MR 1958827 ]
  • Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki and Akira Yoshioka — Star exponential functions for quadratic forms and polar elements [ MR 1958828 ]
  • John Rawnsley — On traces for differential star products on symplectic manifolds [ MR 1958829 ]
  • Joseph Donin — Quantum $G$-manifolds [ MR 1958830 ]
  • J. Donin and A. Mudrov — ${\scr U}_q({\rm sl}(n))$-covariant quantization of symmetric coadjoint orbits via reflection equation algebra [ MR 1958831 ]
  • Olga Radko — Toward a classification of Poisson structures on surfaces [ MR 1958832 ]
  • J. D. S. Jones — Lectures on operads [ MR 1958833 ]
  • Theodore Voronov — Graded manifolds and Drinfeld doubles for Lie bialgebroids [ MR 1958834 ]
  • Dmitry Roytenberg — On the structure of graded symplectic supermanifolds and Courant algebroids [ MR 1958835 ]
  • K. C. H. Mackenzie — On certain canonical diffeomorphisms in symplectic and Poisson geometry [ MR 1958836 ]
  • Hovhannes M. Khudaverdian — Laplacians in odd symplectic geometry [ MR 1958837 ]
  • Y. Kosmann-Schwarzbach and K. C. H. Mackenzie — Differential operators and actions of Lie algebroids [ MR 1958838 ]
  • Long-guang He, Zhang-Ju Liu and De-Shou Zhong — Poisson actions and Lie bialgebroid morphisms [ MR 1958839 ]
  • A. S. Dzhumadil′daev — Identities and derivations for Jacobian algebras [ MR 1958840 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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