Lectures On Duflo Isomorphisms In Lie Algebra And Complex Geometry PDF Download
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Author | : Damien Calaque |
Publisher | : European Mathematical Society |
Total Pages | : 120 |
Release | : 2011 |
Genre | : Cohomology operations |
ISBN | : 9783037190968 |
Download Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry Book in PDF, ePub and Kindle
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.
Author | : DAMIEN CALAQUE; CARLO A. ROSSI. |
Publisher | : |
Total Pages | : 106 |
Release | : |
Genre | : Isomorphisms (Mathematics) |
ISBN | : 9783037195963 |
Download Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry Book in PDF, ePub and Kindle
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. Later on, Duflo's result was refound by Kontsevich in the framework of deformation quantization, who also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. The present book, which arose from a series of lectures by the first author at ETH, derives these two isomorphisms from a Duflo-type result for Q-manifolds. All notions mentioned above are introduced and explained in the book, the only prerequisites being 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 details. The book is well-suited for graduate students in mathematics and mathematical physics as well as for researchers working in Lie theory, algebraic geometry and deformation theory.
Author | : Claudio Carmeli |
Publisher | : European Mathematical Society |
Total Pages | : 308 |
Release | : 2011 |
Genre | : Lie algebras |
ISBN | : 9783037190975 |
Download Mathematical Foundations of Supersymmetry Book in PDF, ePub and Kindle
Supersymmetry is a highly active area of considerable interest among physicists and mathematicians. It is not only fascinating in its own right, but there is also indication that it plays a fundamental role in the physics of elementary particles and gravitation. The purpose of the book is to lay down the foundations of the subject, providing the reader with a comprehensive introduction to the language and techniques, as well as detailed proofs and many clarifying examples. This book is aimed ideally at second-year graduate students. After the first three introductory chapters, the text is divided into two parts: the theory of smooth supermanifolds and Lie supergroups, including the Frobenius theorem, and the theory of algebraic superschemes and supergroups. There are three appendices. The first introduces Lie superalgebras and representations of classical Lie superalgebras, the second collects some relevant facts on categories, sheafification of functors and commutative algebra, and the third explains the notion of Frechet space in the super context.
Author | : Koen Thas |
Publisher | : European Mathematical Society |
Total Pages | : 136 |
Release | : 2012 |
Genre | : Abelian p-groups |
ISBN | : 9783037191101 |
Download A Course on Elation Quadrangles Book in PDF, ePub and Kindle
The notion of elation generalized quadrangle is a natural generalization to the theory of generalized quadrangles of the important notion of translation planes in the theory of projective planes. Almost any known class of finite generalized quadrangles can be constructed from a suitable class of elation quadrangles. In this book the author considers several aspects of the theory of elation generalized quadrangles. Special attention is given to local Moufang conditions on the foundational level, exploring, for instance, Knarr's question from the 1990s concerning the very notion of elation quadrangles. All the known results on Kantor's prime power conjecture for finite elation quadrangles are gathered, some of them published here for the first time. The structural theory of elation quadrangles and their groups is heavily emphasized. Other related topics, such as $p$-modular cohomology, Heisenberg groups, and existence problems for certain translation nets, are briefly touched. This book starts from scratch and is essentially self-contained. Many alternative proofs are given for known theorems. This course contains dozens of exercises at various levels, from very easy to rather difficult, and will stimulate undergraduate and graduate students to enter the fascinating and rich world of elation quadrangles. More accomplished mathematicians will find the final chapters especially challenging.
Author | : Hans Triebel |
Publisher | : European Mathematical Society |
Total Pages | : 120 |
Release | : 2012 |
Genre | : Function spaces |
ISBN | : 9783037191071 |
Download Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration Book in PDF, ePub and Kindle
This book deals first with Haar bases, Faber bases and Faber frames for weighted function spaces on the real line and the plane. It extends results in the author's book, ``Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration'' (EMS, 2010), from unweighted spaces (preferably in cubes) to weighted spaces. The obtained assertions are used to study sampling and numerical integration in weighted spaces on the real line and weighted spaces with dominating mixed smoothness in the plane. A short chapter deals with the discrepancy for spaces on intervals.
Author | : Alexander A. Kirillov |
Publisher | : Cambridge University Press |
Total Pages | : 237 |
Release | : 2008-07-31 |
Genre | : Mathematics |
ISBN | : 0521889693 |
Download An Introduction to Lie Groups and Lie Algebras Book in PDF, ePub and Kindle
This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Author | : Jing-Song Huang |
Publisher | : Springer Science & Business Media |
Total Pages | : 205 |
Release | : 2007-05-27 |
Genre | : Mathematics |
ISBN | : 0817644938 |
Download Dirac Operators in Representation Theory Book in PDF, ePub and Kindle
This book presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective. The book is an excellent contribution to the mathematical literature of representation theory, and this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics.
Author | : Yuri Tschinkel |
Publisher | : Springer Science & Business Media |
Total Pages | : 723 |
Release | : 2010-08-05 |
Genre | : Mathematics |
ISBN | : 0817647457 |
Download Algebra, Arithmetic, and Geometry Book in PDF, ePub and Kindle
EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.
Author | : Pavel Etingof |
Publisher | : American Mathematical Soc. |
Total Pages | : 362 |
Release | : 2016-08-05 |
Genre | : Mathematics |
ISBN | : 1470434415 |
Download Tensor Categories Book in PDF, ePub and Kindle
Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Author | : Alberto S. Cattaneo |
Publisher | : Societe Mathematique de France |
Total Pages | : 210 |
Release | : 2005 |
Genre | : Business & Economics |
ISBN | : |
Download Déformation, quantification, théorie de Lie Book in PDF, ePub and Kindle
In 1997, M. Kontsevich proved that every Poisson manifold admits a formal quantization, canonical up to equivalence. In doing so he solved a longstanding problem in mathematical physics. Through his proof and his interpretation of a later proof given by Tamarkin, he also opened up new research avenues in Lie theory, quantum group theory, deformation theory and the study of operads ... and uncovered fascinating links of these topics with number theory, knot theory and the theory of motives. Without doubt, his work on deformation quantization will continue to influence these fields for many years to come. In the three parts of this volume, we will 1) present the main results of Kontsevich's 1997 preprint and sketch his interpretation of Tamarkin's approach, 2) show the relevance of Kontsevich's theorem for Lie theory and 3) explain the idea from topological string theory which inspired Kontsevich's proof. An appendix is devoted to the geometry of configuration spaces.