EMS Series of Lectures in Mathematics 2011; 114 pp; softcover Volume: 14 ISBN10: 3037190965 ISBN13: 9783037190968 List Price: US$32 Member Price: US$25.60 Order Code: EMSSERLEC/14
 The Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of HarishChandra on semisimple Lie algebras. Kontsevich later refined Duflo's result in the framework of deformation quantization and also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. This book, which arose from a series of lectures by Damien Calaque at ETH, derives these two isomorphisms from a Duflotype result for \(Q\)manifolds. All notions mentioned above are introduced and explained in this book. The only prerequisites are basic linear algebra and differential geometry. In addition to standard notions such as Lie (super) algebras, complex manifolds, Hochschild and ChevalleyEilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in detail. This book is well suited for graduate students in mathematics and mathematical physics as well as researchers working in Lie theory, algebraic geometry, and deformation theory. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in algebra. Table of Contents  Lie algebra cohomology and the Duflo isomorphism
 Hochschild cohomology and spectral sequences
 Dolbeault cohomology and the Kontsevich isomorphism
 Superspaces and Hochschild cohomology
 The DufloKontsevich isomorphism for \(Q\)spaces
 Configuration spaces and integral weights
 The map \(\mathcal{U}_Q\) and its properties
 The map \(\mathcal{H}_Q\) and the homotopy argument
 The explicit form of \(\mathcal{U}_Q\)
 Fedosov resolutions
 Appendix: Deformationtheoretical interpretation of Hochschild cohomology
 Bibliography
 Index
