# Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry

2011-05-15 | ISBN: 3037190965 | PDF | 114 Pages | 3.37 MB

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 Harish-Chandra on semi-simple 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 Duflo-type 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 Chevalley-Eilenberg 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.**Download:**

http://longfiles.com/j1sa4oqjk962/Lectures_on_Duflo_Isomorphisms_in_Lie_Algebra_and_Complex_Geometry.zip.html

**[Fast Download] Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry**

**Ebooks related to "Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry" :**

Empirical Research in Statistics Education

TTC - Understanding Calculus: Problems, Solutions, and Tips [repost]

A Companion to Interdisciplinary Stem Project-Based Learning, Second Edition

Intelligent Mathematics II: Applied Mathematics and Approximation Theory

Advances and Applications in Chaotic Systems

Analysis Now

Mathematical Game Theory and Applications

Operator Algebras, Operator Theory and Applications

Max D. Gunzburger - Finite Element Methods for Viscous Incompressible Flows

Classical Banach Spaces I and II

**Copyright Disclaimer:**

This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.

**Categories**

Astronomy and Cosmology | Physics |

Philosophy | Medicine |

Mathematics |
DSP |

Cryptography | Chemistry |

Biology and Genetics | Psychology and Behavior |

**Popular ebooks**

100 Essential Things You Didn't Know You d(3705)

The Story of Science(3567)

Introducing Mathematics: A Graphic Guide(3428)

How To Learn And Memorize Math, Numbers, E(2961)

Linear Algebra: A Modern Introduction,, 2n(2409)

Encyclopedia of Mathematics(2295)

The Foundations of Mathematics, 2 edition(2280)

Geometric Algebra (Dover Books on Mathemat(2187)

Understanding Statistics(2060)

The Concise Oxford Dictionary of Mathemati(2041)

Applied Mathematics, 4th Edition(1984)

Calculus For Dummies(1952)

Cambridge IGCSE Mathematics: Core & Extend(1938)

Introduction to Logic, 2nd edition(1857)

Geometry for Dummies(1783)