# Infinite Dimensional Algebras and Quantum Integrable Systems (Progress in Mathematics)

Publisher: Birkhäuser Basel

Written in English

## Subjects:

• Mathematics,
• Algebra - Linear,
• Science/Mathematics,
• Applied,
• Group Theory,
• Mathematics / Algebra / General,
• Algebra - General

## Edition Notes

The Physical Object ID Numbers Contributions Petr P. Kulish (Editor), Nenad Manojlovic (Editor), Henning Samtleben (Editor) Format Hardcover Number of Pages 271 Open Library OL9090951M ISBN 10 376437215X ISBN 10 9783764372156

Intuitive meaning. The discovery of quantum groups was quite unexpected since it was known for a long time that compact groups and semisimple Lie algebras are "rigid" objects, in other words, they cannot be "deformed". One of the ideas behind quantum groups is that if we consider a structure that is in a sense equivalent but larger, namely a group algebra or a universal enveloping algebra. 1. Combinatorial representation theory of infinite-dimensional algebras: Kac-Moody algebras, quantum affine algebras, Virasoro and W-algebras and their deformations. 2. Mathematical physics: Exactly solvable systems in statistical mechanics, integrable quantum field theories. My main research interests are Representation theory and Mathematical Physics. This includes the theory of vertex and conformal algebras, representation theory of affine superalgebras, classification of infinite-dimensional groups of supersymmetries and their representations, integrable systems. Venue: in Infinite Dimensional Algebras and Quantum Integrable Systems, eds. P. Kulish, e.a., Progress in Math. Citations: 6 - 2 self.

This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and. ABSTRACT Principal Investigator: Edward Frenkel Proposal Number: Institution: University of California-Berkeley Abstract: Representations of infinite-dimensional Lie algebras and related topics The principal investigator proposes to conduct research in the following areas: local Langlands correspondence for affine Kac--Moody algebras; vertex algebras and quantum groups; cohomology . We plan to hold an international workshop on quantum integrable systems in July, The purpose is to bring together active researchers from around the world and to discuss most recent progress in integrable systems and related mathematical areas. Representation theory of infinite dimensional algebras; Integrable models and combinatorics. The main objective of the laboratory is to develop a common approach to a variety of issues at the interface between the theory of integrable systems and representation theory of quantum and infinite-dimensional groups and algebras.

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This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems'' held in July at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV. International Congress on Mathematical Physics.

‎This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems'' held in July at the University of Algarve, Infinite Dimensional Algebras and Quantum Integrable Systems book, Portugal, as a satellite workshop of the XIV.

International Congress on Mathematical Physics. Recent developments in. Infinite Dimensional Algebras and Quantum Integrable Systems Edward Frenkel (auth.), Petr P. Kulish, Nenad Manojlovich, Henning Samtleben (eds.) This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems'' held in July at the University of Algarve, Faro, Portugal, as a.

Recent developments in the theory of infinite dimensional algebras and their applications to quantum integrable systems are reviewed by some of the leading experts in the field. The volume will be of interest to a broad audience from graduate students to researchers in mathematical physics and related fields.\"--Jacket.

\/span>\" ; \u00A0\u00A0. Get this from a library. Infinite Dimensional Algebras and Quantum Integrable Systems. [Petr P Kulish; Nenad Manojlovich; Henning Samtleben] -- This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems'' held in July at the University of Algarve, Faro, Portugal, as a.

The book is concerned with Kac–Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently self-contained and detailed to be used for graduate courses.

Quantum Integrable Systems and Infinite Dimensional Algebras. February 4 (Wed)(Tue), Symmetric coinvariant algebra and local Weyl module at a double point. is a one- or multiparametric family of operators sharing the eigenfunctions with commuting Hamiltonians of a given quantum integrable system.

The eigenvalues of Q-operator. Quantum Integrable Systems and Inﬁnite Dimensional Algebras February 4 (Wed)–10(Tue), by Research Institute for Mathematical Sciences & Department of Mathmatics, Kyoto University SCHEDULE 4 (wed) - - - - - B.

Feigin D. Lebedev S. Loktev B. Ponsot E. Feigin. A vast and partly overlapping field is the study of integrable systems, classical and quantum systems with an infinite number of conserved quantities (like energy and momentum), but non-local, associated with infinite dimensional symmetry algebras.

Let g be an infinite-dimensional Kac-Moody algebra, and $\hat{U}$ the completion of its universal enveloping algebra with respect to highest weight representations. $\hat{U}$ is a topological Hopf algebra, which appears to have a rather unwieldy Hochschild (coalgebra) cohomology.

17BXX, XX, XX, XX, 16GXX, 16TXX, 81TXX Proceedings Representation Theory Infinite-Dimensional Lie Groups and Algebras Functional Analysis Integrable Systems Algebraic Geometry Number Theory Quantum Groups Superalgebras and Supergroups Symmetries in String Theory Supergravity Conformal Field Theories Nonrelativistic Theories.

This chapter focuses on KdV-type equations and W-algebras. There exists a remarkable connection between the conformal field theory and the theory of KdV-type equations. The symmetry generators in conformal field theory form an associative infinite-dimensional algebra which always contains the Virasoro algebra as a subalgebra.

Description; Chapters; Supplementary; The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July As a continuation of the RIMS Research Project “Method of Algebraic Analysis in Integrable Systems” inthe workshop's aim was to cover exciting new developments that have emerged.

This book investigates the high degree of symmetry that lies hidden in integrable systems. To that end, differential equations arising from classical mechanics, such as the KdV equation and the KP equations, are used here by the authors to introduce the notion of an infinite dimensional transformation group acting on spaces of integrable systems.

Looking for an examination copy. If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact [email protected] providing details of the course you are teaching. This is the third, substantially revised edition of.

fundamen tal 2-dimensional irreducible represe n ta t io n of the algebra (4 4) (actually, they also pro vide the fundamen t a l represe n ta t io n of the generators of sl (2) alge- bra (45)). During the last thirty years, the representation theory of infinite-dimensional Lie algebras has been one of the most prolific areas of modern mathematics, and has developed deep connections with many other areas of pure mathematics and mathematical physics, including algebraic geometry, integrable systems, quantum field theory, statistical mechanics, and combinatorics.

This volume begins with an introduction to the structure of finite-dimensional simple Lie algebras, including the representation of ${\\widehat {\\mathfrak {sl}}}(2, {\\mathbb C})$, 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.

Quantum Integrable Systems: Construction, Solution, Algebraic Aspect Anjan Kundu Saha Institute of Nuclear Physics Theory Group 1/AF Bidhan Nagar,Calcutta ,India.

Abstract Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal. Infinite Dimensional Algebras and Quantum Integrable Systems Book This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems" held in July at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV International Congress on Mathematical Physics.

The book is far from elementary and is suitable for researchers and graduate students with a good knowledge of intersection theory and geometric invariant theory. Starting with this knowledge, it surveys most of the known results and theories of the Hilbert schemes of points, implying infinite dimensional Lie Algebras and their actions.

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.

They find applications in the theory of affine Lie algebras, Kac-Moody Lie algebras (central extensions), completely integrable systems, soliton equations (Toda, KdV, KP), and quantum field theory; see, for example, and Section 5.

Central extensions of loop algebras are examples of infinite-dimensional Lie algebras which need not have a. Although complete integrability is a non-generic property of general dynamical systems, many systems appearing in physics are completely integrable, in the Hamiltonian sense, the key example being multi-dimensional harmonic oscillators.

Another standard example is planetary motion about either one fixed center (e.g., the sun) or two. Other elementary examples include the motion of a rigid body. A new class of infinite-dimensional Lie algebras, called Lax operator algebras, is presented, along with a related unifying approach to finite- dimensional integrable systems with a spectral parameter on a Riemann surface such as the Calogero–Moser and Hitchin systems.

The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given exotic cohomology of the symmetry algebras opens a way to formulate such conditions in internal terms of the pde s under the study.

In this paper we consider certain examples of infinite-dimensional Lie algebras with nontrivial second exotic. : New Trends in Quantum Integrable Systems - Proceedings of the Infinite Analysis 09 (): Feigin, Boris, Jimbo, Michio, Okado, Masato: Books.

They have also found applications in such fields as algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics.

This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship between vertex algebras and the geometry of algebraic curves. Get Book. The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July As a continuation of the RIMS Research Project "Method of Algebraic Analysis in Integrable Systems" inthe workshop's aim was to cover exciting new developments that.

Integrable Systems, Quantum Groups, and Quantum Field Theories L. Faddeev (auth.), L. Ibort, M. Rodríguez (eds.) In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics.

integrable systems. holonomic quantum fields. Types of quantum field thories similarly we avoided the relevant books on Kac-Moody algebras and groups but included the books on related VOAs and the M.

Jimbo, E. Date, Solitons: Differential equations, symmetries and infinite dimensional algebras, Cambridge Tracts in Mathematics “Integrable systems” and “algebraic geometry” are two classical fields in Mathematics and historically they have had fruitful interactions which have enriched both Mathematics and Theoretical Physics.

This volume discusses recent developments of these two fields and also the .This special issue is centred around the workshop Infinite Dimensional Algebras and Quantum Integrable Systems II—IDAQUISheld at the University of Algarve, Faro, Portugal in July It was the second workshop in the IDAQUIS series following a previous meeting at the same location in The latest workshop gathered around forty experts in the field reviewing recent developments.