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

• B. Fedosov -- Deformation quantization: Pro and contra
• N. P. Landsman -- Quantization as a functor
• H. Omori, Y. Maeda, N. Miyazaki, and A. Yoshioka -- Star exponential functions for quadratic forms and polar elements
• J. Rawnsley -- On traces for differential star products on symplectic manifolds
• J. Donin -- Quantum \(G\)-manifolds
• J. Donin and A. Mudrov -- \(\mathcal{U}_q(sl(n))\)-covariant quantization of symmetric coadjoint orbits via reflection equation algebra
• O. Radko -- Toward a classification of Poisson structures on surfaces
• J. D. S. Jones -- Lectures on operads
• T. Voronov -- Graded manifolds and Drinfeld doubles for Lie bialgebroids
• D. Roytenberg -- On the structure of graded symplectic supermanifolds and Courant algebroids
• K. C. H. Mackenzie -- On certain canonical diffeomorphisms in symplectic and Poisson geometry
• H. M. Khudaverdian -- Laplacians in odd symplectic geometry
• Y. Kosmann-Schwarzbach and K. C. H. Mackenzie -- Differential operators and actions of Lie algebroids
• L.-g. He, Z.-J. Liu, and D.-S. Zhong -- Poisson actions and Lie bialgebroid morphisms
• A. S. Dzhumadil'daev -- Identities and derivations for Jacobian algebras