Dictionary On Lie Algebras And Superalgebras

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Dictionary on Lie Algebras and Superalgebras

Author : Luc Frappat
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Dictionary on Lie Algebras and Superalgebras by : Luc Frappat

Download or read book Dictionary on Lie Algebras and Superalgebras written by Luc Frappat and published by . This book was released on 2000 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a detailed reference on Lie algebras and Lie superalgebras presented in the form of a dictionary. It is intended to be useful to mathematical and theoretical physicists, from the level of the graduate student upwards. The Dictionary will serve as the reference of choice for practitioners and students alike. Key Features: * Compiles and presents material currently scattered throughout numerous textbooks and specialist journal articles * Dictionary format provides an easy to use reference on the essential topics concerning Lie algebras and Lie superalgebras * Covers the structure of Lie algebras and Lie superalgebras and their finite dimensional representation theory * Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras

Lie Algebras and Lie Groups

Author : Jean-Pierre Serre
Publisher : Springer
ISBN 13 : 3540706348
Total Pages : 180 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Lie Algebras and Lie Groups by : Jean-Pierre Serre

Download or read book Lie Algebras and Lie Groups written by Jean-Pierre Serre and published by Springer. This book was released on 2009-02-07 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I.I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups. of time prevented me from including the more precise theory of Lack semisimple Lie algebras (roots, weights, etc.); but, at least, I have given, as a last Chapter, the typical case ofal, . This part has been written with the help of F. Raggi and J. Tate. I want to thank them, and also Sue Golan, who did the typing for both parts. Jean-Pierre Serre Harvard, Fall 1964 Chapter I. Lie Algebras: Definition and Examples Let Ie be a commutativering with unit element, and let A be a k-module, then A is said to be a Ie-algebra if there is given a k-bilinear map A x A~ A (i.e., a k-homomorphism A0" A -+ A). As usual we may define left, right and two-sided ideals and therefore quo tients. Definition 1. A Lie algebra over Ie isan algebrawith the following properties: 1). The map A0i A -+ A admits a factorization A ®i A -+ A2A -+ A i.e., ifwe denote the imageof(x, y) under this map by [x, y) then the condition becomes for all x e k. [x, x)=0 2). (lx, II], z]+ny, z), x) + ([z, xl, til = 0 (Jacobi's identity) The condition 1) implies [x,1/]=-[1/, x).

Dualities and Representations of Lie Superalgebras

Author : Shun-Jen Cheng
Publisher : American Mathematical Soc.
ISBN 13 : 0821891189
Total Pages : 323 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Dualities and Representations of Lie Superalgebras by : Shun-Jen Cheng

Download or read book Dualities and Representations of Lie Superalgebras written by Shun-Jen Cheng and published by American Mathematical Soc.. This book was released on 2012 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a systematic account of the structure and representation theory of finite-dimensional complex Lie superalgebras of classical type and serves as a good introduction to representation theory of Lie superalgebras. Several folklore results are rigorously proved (and occasionally corrected in detail), sometimes with new proofs. Three important dualities are presented in the book, with the unifying theme of determining irreducible characters of Lie superalgebras. In order of increasing sophistication, they are Schur duality, Howe duality, and super duality. The combinatorics of symmetric functions is developed as needed in connections to Harish-Chandra homomorphism as well as irreducible characters for Lie superalgebras. Schur-Sergeev duality for the queer Lie superalgebra is presented from scratch with complete detail. Howe duality for Lie superalgebras is presented in book form for the first time. Super duality is a new approach developed in the past few years toward understanding the Bernstein-Gelfand-Gelfand category of modules for classical Lie superalgebras. Super duality relates the representation theory of classical Lie superalgebras directly to the representation theory of classical Lie algebras and thus gives a solution to the irreducible character problem of Lie superalgebras via the Kazhdan-Lusztig polynomials of classical Lie algebras.

The Theory of Lie Superalgebras

Author : M. Scheunert
Publisher : Springer
ISBN 13 : 3540352864
Total Pages : 280 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Theory of Lie Superalgebras by : M. Scheunert

Download or read book The Theory of Lie Superalgebras written by M. Scheunert and published by Springer. This book was released on 2006-11-15 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Unconventional Lie Algebras

Author : D. B. Fuks
Publisher : American Mathematical Soc.
ISBN 13 : 9780821841211
Total Pages : 234 pages
Book Rating : 4.8/5 (412 download)

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Book Synopsis Unconventional Lie Algebras by : D. B. Fuks

Download or read book Unconventional Lie Algebras written by D. B. Fuks and published by American Mathematical Soc.. This book was released on 1993 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Groups and Lie Algebras

Author : B.P. Komrakov
Publisher : Springer Science & Business Media
ISBN 13 : 9401152586
Total Pages : 442 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Lie Groups and Lie Algebras by : B.P. Komrakov

Download or read book Lie Groups and Lie Algebras written by B.P. Komrakov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection contains papers conceptually related to the classical ideas of Sophus Lie (i.e., to Lie groups and Lie algebras). Obviously, it is impos sible to embrace all such topics in a book of reasonable size. The contents of this one reflect the scientific interests of those authors whose activities, to some extent at least, are associated with the International Sophus Lie Center. We have divided the book into five parts in accordance with the basic topics of the papers (although it can be easily seen that some of them may be attributed to several parts simultaneously). The first part (quantum mathematics) combines the papers related to the methods generated by the concepts of quantization and quantum group. The second part is devoted to the theory of hypergroups and Lie hypergroups, which is one of the most important generalizations of the classical concept of locally compact group and of Lie group. A natural harmonic analysis arises on hypergroups, while any abstract transformation of Fourier type is gen erated by some hypergroup (commutative or not). Part III contains papers on the geometry of homogeneous spaces, Lie algebras and Lie superalgebras. Classical problems of the representation theory for Lie groups, as well as for topological groups and semigroups, are discussed in the papers of Part IV. Finally, the last part of the collection relates to applications of the ideas of Sophus Lie to differential equations.

Introduction to Lie Algebras

Author : K. Erdmann
Publisher : Springer Science & Business Media
ISBN 13 : 1846284902
Total Pages : 254 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Introduction to Lie Algebras by : K. Erdmann

Download or read book Introduction to Lie Algebras written by K. Erdmann and published by Springer Science & Business Media. This book was released on 2006-09-28 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.

Infinite-dimensional Lie Algebras

Author : Minoru Wakimoto
Publisher : American Mathematical Soc.
ISBN 13 : 9780821826546
Total Pages : 332 pages
Book Rating : 4.8/5 (265 download)

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Book Synopsis Infinite-dimensional Lie Algebras by : Minoru Wakimoto

Download or read book Infinite-dimensional Lie Algebras written by Minoru Wakimoto and published by American Mathematical Soc.. This book was released on 2001 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume begins with an introduction to the structure of finite-dimensional simple Lie algebras, including the representation of ...... root systems, the Cartan matrix, and a Dynkin diagram of a finite-dimensional simple Lie algebra. Continuing on, the main subjects of the book are the structure (real and imaginary root systems) of and the character formula for Kac-Moody superalgebras, which is explained in a very general setting. Only elementary linear algebra and group theory are assumed. Also covered is modular property and asymptotic behavior of integrable characters of affine Lie algebras. The exposition is self-contained and includes examples. The book can be used in a graduate-level course on the topic.

General Theory of Lie Algebras

Author : Yutze Chow
Publisher : CRC Press
ISBN 13 : 9780677038902
Total Pages : 468 pages
Book Rating : 4.0/5 (389 download)

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Book Synopsis General Theory of Lie Algebras by : Yutze Chow

Download or read book General Theory of Lie Algebras written by Yutze Chow and published by CRC Press. This book was released on 1978 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in Lie Superalgebras

Author : Maria Gorelik
Publisher : Springer Science & Business
ISBN 13 : 3319029525
Total Pages : 281 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Advances in Lie Superalgebras by : Maria Gorelik

Download or read book Advances in Lie Superalgebras written by Maria Gorelik and published by Springer Science & Business. This book was released on 2014-04-28 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is the outcome of the conference "Lie superalgebras," which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held provided comprehensive insights into the newest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field and provides a complete account of the newest trends in research on Lie Superalgebras.

Modular Lie Algebras and their Representations

Author : H. Strade
Publisher : CRC Press
ISBN 13 : 1000103390
Total Pages : 318 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Modular Lie Algebras and their Representations by : H. Strade

Download or read book Modular Lie Algebras and their Representations written by H. Strade and published by CRC Press. This book was released on 2020-08-11 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic. It introduces the beginner to the theory of modular Lie algebras and is meant to be a reference text for researchers.

Lie Algebras and Locally Compact Groups

Author : Irving Kaplansky
Publisher : University of Chicago Press
ISBN 13 : 0226424537
Total Pages : 161 pages
Book Rating : 4.2/5 (264 download)

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Book Synopsis Lie Algebras and Locally Compact Groups by : Irving Kaplansky

Download or read book Lie Algebras and Locally Compact Groups written by Irving Kaplansky and published by University of Chicago Press. This book was released on 1971 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, "Lie Algebras," the structure theory of semi-simple Lie algebras in characteristic zero is presented, following the ideas of Killing and Cartan. Chapter 2, "The Structure of Locally Compact Groups," deals with the solution of Hilbert's fifth problem given by Gleason, Montgomery, and Zipplin in 1952.

Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras

Author : Victor G. Kac
Publisher : World Scientific
ISBN 13 : 9814522201
Total Pages : 250 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras by : Victor G. Kac

Download or read book Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras written by Victor G. Kac and published by World Scientific. This book was released on 2013 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras--such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations--simplify and clarify the constructions of the first edition of the book. -- Cover.

Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics

Author : Kailash C. Misra
Publisher : American Mathematical Soc.
ISBN 13 : 1470418444
Total Pages : 370 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics by : Kailash C. Misra

Download or read book Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics written by Kailash C. Misra and published by American Mathematical Soc.. This book was released on 2016-06-28 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.

Notes on Lie Algebras

Author : Hans Samelson
Publisher : Springer Science & Business Media
ISBN 13 : 1461390141
Total Pages : 172 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Notes on Lie Algebras by : Hans Samelson

Download or read book Notes on Lie Algebras written by Hans Samelson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Cartan sub Lie algebra, roots, Weyl group, Dynkin diagram, . . . ) and the classification, as found by Killing and Cartan (the list of all semisimple Lie algebras consists of (1) the special- linear ones, i. e. all matrices (of any fixed dimension) with trace 0, (2) the orthogonal ones, i. e. all skewsymmetric ma trices (of any fixed dimension), (3) the symplectic ones, i. e. all matrices M (of any fixed even dimension) that satisfy M J = - J MT with a certain non-degenerate skewsymmetric matrix J, and (4) five special Lie algebras G2, F , E , E , E , of dimensions 14,52,78,133,248, the "exceptional Lie 4 6 7 s algebras" , that just somehow appear in the process). There is also a discus sion of the compact form and other real forms of a (complex) semisimple Lie algebra, and a section on automorphisms. The third chapter brings the theory of the finite dimensional representations of a semisimple Lie alge bra, with the highest or extreme weight as central notion. The proof for the existence of representations is an ad hoc version of the present standard proof, but avoids explicit use of the Poincare-Birkhoff-Witt theorem. Complete reducibility is proved, as usual, with J. H. C. Whitehead's proof (the first proof, by H. Weyl, was analytical-topological and used the exis tence of a compact form of the group in question). Then come H.

Lie Algebras and Their Representations

Author : Seok-Jin Kang
Publisher : American Mathematical Soc.
ISBN 13 : 9780821855317
Total Pages : 244 pages
Book Rating : 4.8/5 (553 download)

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Book Synopsis Lie Algebras and Their Representations by : Seok-Jin Kang

Download or read book Lie Algebras and Their Representations written by Seok-Jin Kang and published by American Mathematical Soc.. This book was released on 1996 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the refereed proceedings of the symposium on Lie algebras and representation theory which was held at Seoul National University (Korea) in January 1995. The symposium was sponsored by the Global Analysis Research Center of Seoul National University. Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area. Consequently, this book can serve both as an introduction to various aspects of the theory of Lie algebras and their representations and as a good reference work for further research.

Classification and Identification of Lie Algebras

Author : Libor Šnob
Publisher : American Mathematical Soc.
ISBN 13 : 147043654X
Total Pages : 306 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Classification and Identification of Lie Algebras by : Libor Šnob

Download or read book Classification and Identification of Lie Algebras written by Libor Šnob and published by American Mathematical Soc.. This book was released on 2017-04-05 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain classes of nilpotent and solvable Lie algebras of arbitrary finite dimensions for which complete or partial classification exists and discuss in detail their construction and properties. The book is based on material that was previously dispersed in journal articles, many of them written by one or both of the authors together with their collaborators. The reader of this book should be familiar with Lie algebra theory at an introductory level.