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Cohomology Of Infinite Dimensional Lie Algebras
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Book Synopsis Cohomology of Infinite-Dimensional Lie Algebras by : D.B. Fuks
Download or read book Cohomology of Infinite-Dimensional Lie Algebras written by D.B. Fuks and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is no question that the cohomology of infinite dimensional Lie algebras deserves a brief and separate mono graph. This subject is not cover~d by any of the tradition al branches of mathematics and is characterized by relative ly elementary proofs and varied application. Moreover, the subject matter is widely scattered in various research papers or exists only in verbal form. The theory of infinite-dimensional Lie algebras differs markedly from the theory of finite-dimensional Lie algebras in that the latter possesses powerful classification theo rems, which usually allow one to "recognize" any finite dimensional Lie algebra (over the field of complex or real numbers), i.e., find it in some list. There are classifica tion theorems in the theory of infinite-dimensional Lie al gebras as well, but they are encumbered by strong restric tions of a technical character. These theorems are useful mainly because they yield a considerable supply of interest ing examples. We begin with a list of such examples, and further direct our main efforts to their study.
Book Synopsis Infinite Dimensional Groups with Applications by : Victor Kac
Download or read book Infinite Dimensional Groups with Applications written by Victor Kac and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume records most of the talks given at the Conference on Infinite-dimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10-May 15, 1984, as a part of the special program on Kac-Moody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinite-dimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general Kac-Moody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my thanks to the MSRI for sponsoring the meeting, to Ms. Faye Yeager for excellent typing, to the authors for their manuscripts, and to Springer-Verlag for publishing this volume. V. Kac INFINITE DIMENSIONAL GROUPS WITH APPLICATIONS CONTENTS The Lie Group Structure of M. Adams. T. Ratiu 1 Diffeomorphism Groups and & R. Schmid Invertible Fourier Integral Operators with Applications On Landau-Lifshitz Equation and E. Date 71 Infinite Dimensional Groups Flat Manifolds and Infinite D. S. Freed 83 Dimensional Kahler Geometry Positive-Energy Representations R. Goodman 125 of the Group of Diffeomorphisms of the Circle Instantons and Harmonic Maps M. A. Guest 137 A Coxeter Group Approach to Z. Haddad 157 Schubert Varieties Constructing Groups Associated to V. G. Kac 167 Infinite-Dimensional Lie Algebras I. Kaplansky 217 Harish-Chandra Modules Over the Virasoro Algebra & L. J. Santharoubane 233 Rational Homotopy Theory of Flag S.
Book Synopsis Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics by : Josi A. de Azcárraga
Download or read book Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics written by Josi A. de Azcárraga and published by Cambridge University Press. This book was released on 1998-08-06 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.
Book Synopsis Hilbert Schemes of Points and Infinite Dimensional Lie Algebras by : Zhenbo Qin
Download or read book Hilbert Schemes of Points and Infinite Dimensional Lie Algebras written by Zhenbo Qin and published by American Mathematical Soc.. This book was released on 2018-02-26 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes of collections of points (zero-dimensional subschemes) in a smooth algebraic surface . Schemes turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of , including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of and the Gromov–Witten correspondence. The last part of the book presents results about quantum cohomology of and related questions. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, combinatorics, topology, number theory, and theoretical physics.
Book Synopsis Infinite Dimensional Lie Algebras and Groups by : V G Kac
Download or read book Infinite Dimensional Lie Algebras and Groups written by V G Kac and published by World Scientific. This book was released on 1989-07-01 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:Integrable Representation of Kac-Moody Algebras: Results and Open Problems (V Chari & A Pressley)Existence of Certain Components in the Tensor Product of Two Integrable Highest Weight Modules for Kac-Moody Algebras (SKumar)Frobenius Action on the B-Cohomology (O Mathieu)Certain Rank Two Subsystems of Kac-Moody Root Systems (J Morita)Lie Groups Associated to Kac-Moody Lie Algebras: An Analytic Approach (E Rodriguez-Carrington)Almost Split-K-Forms of Kac-Moody Algebras (G Rousseau)Global Representations of the Diffeomorphism Groups of the Circle (F Bien)Path Space Realization of the Basic Representation of An(1) (E Date et al)Boson-Fermion Correspondence Over (C De Concini et al)Classification of Modular Invariant Representations of Affine Algebras (V G Kac & M Wakimoto)Standard Monomial Theory for SL2 (V Lakshmibai & C S Seshadri)Some Results on Modular Invariant Representations (S Lu)Current Algebras in 3+1 Space-Time Dimensions (J Mickelson)Standard Representations of An(1) (M Primc)Representations of the Algebra Uq(sI(2)), q-Orthogonal Polynomials and Invariants of Links (A N Kirillov & N Yu Reshetikhin)Infinite Super Grassmannians and Super Plücker Equations (M J Bergvelt)Drinfeld-Sokolov Hierarchies and t-Functions (H J Imbens)Super Boson-Fermion Correspondence of Type B (V G Kac & J W van de Leur)Prym Varieties and Soliton Equations (T Shiota)Polynomial Solutions of the BKP Hierarchy and Projective Representations of Symmetric Groups (Y You)Toward Generalized Macdonald's Identities (D Bernard)Conformal Theories with Non-Linearly Extended Virasoro Symmetries and Lie Algebra Classification (A Bilal & J-LGervais)Extended Conformal Algebras from Kac-Moody Algebras (P Bouwknegt)Meromorphic Conformal Field Theory (P Goddard)Local Extensions of the U(1) Current Algebra and Their Positive Energy Representations (R R Paunov & I T Todorov)Conformal Field Theory on Moduli Family of Stable Curves with Gauge Symmetries (A Tsuchiya & Y Yamada) Readership: Mathematicians and mathematical physicists
Book Synopsis Homological Algebra by : S.I. Gelfand
Download or read book Homological Algebra written by S.I. Gelfand and published by Springer Science & Business Media. This book was released on 1994-03-29 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.
Book Synopsis Infinite-Dimensional Lie Algebras by : Victor G. Kac
Download or read book Infinite-Dimensional Lie Algebras written by Victor G. Kac and published by Cambridge University Press. This book was released on 1990 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third, substantially revised edition of a monograph concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie albegras, and their representations, based on courses given over a number of years at MIT and in Paris.
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 Nature. This book was released on 2022-01-05 with total page 245 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 Introduction to Finite and Infinite Dimensional Lie (Super)algebras by : Neelacanta Sthanumoorthy
Download or read book Introduction to Finite and Infinite Dimensional Lie (Super)algebras written by Neelacanta Sthanumoorthy and published by Academic Press. This book was released on 2016-04-26 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras
Book Synopsis Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory by : Stephen Berman
Download or read book Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory written by Stephen Berman and published by American Mathematical Soc.. This book was released on 2002 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, ``Infinite-Dimensional Lie Theory and Conformal Field Theory'', held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field. Thisconference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual interest. The talks focused on recent developments in the representation theory of affine, quantum affine, and extended affine Lie algebras and Lie superalgebras. They also highlightedapplications to conformal field theory, integrable and disordered systems. Some of the articles are expository and accessible to a broad readership of mathematicians and physicists interested in this area; others are research articles that are appropriate for more advanced readers.
Book Synopsis Infinite-dimensional Lie algebras by : R.K. Amayo
Download or read book Infinite-dimensional Lie algebras written by R.K. Amayo and published by Springer. This book was released on 2014-01-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is only in recent times that infinite-dimensional Lie algebras have been the subject of other than sporadic study, with perhaps two exceptions: Cartan's simple algebras of infinite type, and free algebras. However, the last decade has seen a considerable increase of interest in the subject, along two fronts: the topological and the algebraic. The former, which deals largely with algebras of operators on linear spaces, or on manifolds modelled on linear spaces, has been dealt with elsewhere*). The latter, which is the subject of the present volume, exploits the surprising depth of analogy which exists between infinite-dimen sional Lie algebras and infinite groups. This is not to say that the theory consists of groups dressed in Lie-algebraic clothing. One of the tantalising aspects of the analogy, and one which renders it difficult to formalise, is that it extends to theorems better than to proofs. There are several cases where a true theorem about groups translates into a true theorem about Lie algebras, but where the group-theoretic proof uses methods not available for Lie algebras and the Lie-theoretic proof uses methods not available for groups. The two theories tend to differ in fine detail, and extra variations occur in the Lie algebra case according to the underlying field. Occasionally the analogy breaks down altogether. And of course there are parts of the Lie theory with no group-theoretic counterpart.
Book Synopsis Infinite Dimensional Lie Algebras by : Victor G. Kac
Download or read book Infinite Dimensional Lie Algebras written by Victor G. Kac and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Infinite Dimensional Lie Groups in Geometry and Representation Theory by : Augustin Banyaga
Download or read book Infinite Dimensional Lie Groups in Geometry and Representation Theory written by Augustin Banyaga and published by World Scientific. This book was released on 2002-07-12 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 2000 Howard conference on “Infinite Dimensional Lie Groups in Geometry and Representation Theory”. It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and established researchers in the field of geometry and its applications to mathematical physics. Contents:Inheritance Properties for Lipschitz-Metrizable Frölicher Groups (J Teichmann)Around the Exponential Mapping (T Robart)On a Solution to a Global Inverse Problem with Respect to Certain Generalized Symmetrizable Kac-Moody Algebras (J A Leslie)The Lie Group of Fourier Integral Operators on Open Manifolds (R Schmid)On Some Properties of Leibniz Algebroids (A Wade)On the Geometry of Locally Conformal Symplectic Manifolds (A Banyaga)Some Properties of Locally Conformal Symplectic Manifolds (S Haller)Criticality of Unit Contact Vector Fields (P Rukimbira)Orbifold Homeomorphism and Diffeomorphism Groups (J E Borzellino & V Brunsden)A Note on Isotopies of Symplectic and Poisson Structures (A Banyaga & P Donato)Remarks on Actions on Compacta by Some Infinite-Dimensional Groups (V Pestov) Readership: Graduate students and researchers in mathematics and mathematical physics. Keywords:
Book Synopsis Differential Topology, Infinite-Dimensional Lie Algebras, and Applications by : Alexander Astashkevich
Download or read book Differential Topology, Infinite-Dimensional Lie Algebras, and Applications written by Alexander Astashkevich and published by American Mathematical Soc.. This book was released on 1999 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents contributions by leading experts in the field. The articles are dedicated to D.B. Fuchs on the occasion of his 60th birthday. Contributors to the book were directly influenced by Professor Fuchs, and include his students, friends, and professional colleagues. In addition to their research, they offer personal reminicences about Professor Fuchs, giving insight into the history of Russian mathematics.
Book Synopsis Deformation Theory of Algebras and Structures and Applications by : Michiel Hazewinkel
Download or read book Deformation Theory of Algebras and Structures and Applications written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 1024 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a result of a meeting which took place in June 1986 at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting. In particular it is now abundantly clear that the Deformation theory of algebras is indeed central to the whole philosophy of deformations/perturbations/stability. This is one of the main results of the 254 page paper below (practically a book in itself) by Gerstenhaber and Shack entitled "Algebraic cohomology and defor mation theory". Two of the main philosphical-methodological pillars on which deformation theory rests are the fol lowing • (Pure) To study a highly complicated object, it is fruitful to study the ways in which it can arise as a limit of a family of simpler objects: "the unraveling of complicated structures" . • (Applied) If a mathematical model is to be applied to the real world there will usually be such things as coefficients which are imperfectly known. Thus it is important to know how the behaviour of a model changes as it is perturbed (deformed).
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 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lie Algebras, Cohomology, and New Applications to Quantum Mechanics by : Niky Kamran
Download or read book Lie Algebras, Cohomology, and New Applications to Quantum Mechanics written by Niky Kamran and published by American Mathematical Soc.. This book was released on 1994 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.
