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Yangians And Classical Lie Algebras
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Book Synopsis Yangians and Classical Lie Algebras by : Alexander Molev
Download or read book Yangians and Classical Lie Algebras written by Alexander Molev and published by American Mathematical Soc.. This book was released on 2007 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St. Petersburg's school of mathematical physics in the 1980s. This book is an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras.
Book Synopsis Sugawara Operators for Classical Lie Algebras by : Alexander Molev:
Download or read book Sugawara Operators for Classical Lie Algebras written by Alexander Molev: and published by American Mathematical Soc.. This book was released on 2018-02-28 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical -algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connects the Sugawara operators with the classical -algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.
Book Synopsis Stability in Modules for Classical Lie Algebras by : Georgia Benkart
Download or read book Stability in Modules for Classical Lie Algebras written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 1990 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last century, mathematicians and physicists alike have studied extensively the finite dimensional irreducible representations of complex classical Lie algebras. These studies have led to numerous formulas for computing the dimensions, weights, weight multiplicities, and tensor products of the representations. The dependence of these quantities on the rank of the Lie algebra has been revealed in recent investigations using Schur functions and characters.
Download or read book Lie Algebras written by Zhe-Xian Wan and published by Elsevier. This book was released on 2014-07-10 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie Algebras is based on lectures given by the author at the Institute of Mathematics, Academia Sinica. This book discusses the fundamentals of the Lie algebras theory formulated by S. Lie. The author explains that Lie algebras are algebraic structures employed when one studies Lie groups. The book also explains Engel's theorem, nilpotent linear Lie algebras, as well as the existence of Cartan subalgebras and their conjugacy. The text also addresses the Cartan decompositions and root systems of semi-simple Lie algebras and the dependence of structure of semi-simple Lie algebras on root systems. The text explains in details the fundamental systems of roots of semi simple Lie algebras and Weyl groups including the properties of the latter. The book addresses the group of automorphisms and the derivation algebra of a Lie algebra and Schur's lemma. The book then shows the characters of irreducible representations of semi simple Lie algebras. This book can be useful for students in advance algebra or who have a background in linear algebra.
Book Synopsis Lie Groups, Lie Algebras, and Some of Their Applications by : Robert Gilmore
Download or read book Lie Groups, Lie Algebras, and Some of Their Applications written by Robert Gilmore and published by Courier Corporation. This book was released on 2012-05-23 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.
Book Synopsis Classical Lie Algebras at Infinity by : Ivan Penkov
Download or read book Classical Lie Algebras at Infinity written by Ivan Penkov and published by Springer. This book was released on 2023-01-07 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Book Synopsis A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods by : Johan G. F. Belinfante
Download or read book A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods written by Johan G. F. Belinfante and published by SIAM. This book was released on 1989-01-01 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the concepts and methods of the Lie theory in a form accessible to the non-specialist by keeping mathematical prerequisites to a minimum. Although the authors have concentrated on presenting results while omitting most of the proofs, they have compensated for these omissions by including many references to the original literature. Their treatment is directed toward the reader seeking a broad view of the subject rather than elaborate information about technical details. Illustrations of various points of the Lie theory itself are found throughout the book in material on applications. In this reprint edition, the authors have resisted the temptation of including additional topics. Except for correcting a few minor misprints, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed.
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.
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.
Download or read book Lie Theory written by Jean-Philippe Anker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: * First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.
Download or read book Lie Groups written by Claudio Procesi and published by Springer Science & Business Media. This book was released on 2007-10-17 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. In Lie Groups: An Approach through Invariants and Representations, the author's masterful approach gives the reader a comprehensive treatment of the classical Lie groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis. By covering sufficient background material, the book is made accessible to a reader with a relatively modest mathematical background. Historical information, examples, exercises are all woven into the text. This unique exposition is suitable for a broad audience, including advanced undergraduates, graduates, mathematicians in a variety of areas from pure algebra to functional analysis and mathematical physics.
Download or read book Handbook of Algebra written by and published by Elsevier. This book was released on 2003-10-15 with total page 1184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Algebra
Book Synopsis Representations of Shifted Yangians and Finite $W$-algebras by : Jonathan Brundan
Download or read book Representations of Shifted Yangians and Finite $W$-algebras written by Jonathan Brundan and published by American Mathematical Soc.. This book was released on 2008 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study highest weight representations of shifted Yangians over an algebraically closed field of characteristic $0$. In particular, they classify the finite dimensional irreducible representations and explain how to compute their Gelfand-Tsetlin characters in terms of known characters of standard modules and certain Kazhdan-Lusztig polynomials. The authors' approach exploits the relationship between shifted Yangians and the finite W-algebras associated to nilpotent orbits in general linear Lie algebras.
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.
Book Synopsis Asymptotic Combinatorics with Application to Mathematical Physics by : V.A. Malyshev
Download or read book Asymptotic Combinatorics with Application to Mathematical Physics written by V.A. Malyshev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.
Book Synopsis The Monster and Lie Algebras by : Joseph Ferrar
Download or read book The Monster and Lie Algebras written by Joseph Ferrar and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thisseries is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.
Book Synopsis Lie Groups, Lie Algebras, and Cohomology by : Anthony W. Knapp
Download or read book Lie Groups, Lie Algebras, and Cohomology written by Anthony W. Knapp and published by Princeton University Press. This book was released on 1988-05-21 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations. Along the way it develops the computational techniques that are so important in handling Lie groups. The book is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986 to an audience having little or no background in Lie groups but interested in seeing connections among algebra, geometry, and Lie theory. These notes develop what is needed beyond a first graduate course in algebra in order to appreciate cohomological induction and to see its first consequences. Along the way one is able to study homological algebra with a significant application in mind; consequently one sees just what results in that subject are fundamental and what results are minor.
