Full text get a printable copy pdf file of the complete article 611k, or click on a page image below to browse page by page. Bombay lectures on highest weight representations if infinite dimensional lie algebras subject. Infinitedimensional lie groups and algebras in mathematical. Deformations of some infinitedimensional lie algebras. These lie algebras, which we call here lie algebras of type l, arose as one. Infinite dimensional lie algebras an introduction progress in. Descargar infinitedimensional lie algebras en pdf libros. Kac massachusettsinstitute oftechnology, usa ashokk.
A clear account of kacmoody algebras by one of the founders. Infinite dimensional lie groups and algebras in mathematical physics this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We show how various extensions of the ordinary galilei algebra can be obtained by truncations and contractions, in some cases via an affine kac moody algebra. These sections were based on material in kac and rainas book \bombay lectures on highest weight representations of in nite dimensional lie algebras 4. Application to the classification of finite order automorphisms. It is a kac moody algebra for which the generalized cartan matrix is positive semidefinite and has corank 1. Adamovic, drazen kac, victor g moseneder frajria, pierluigi papi, paolo and perse, ozren 2018.
A new class of unitarizable highest weight representations of infinitedimensional lie algebras, ii by hans plesner jakobsen and victor kac download pdf 987 kb. V kac at tata institute, india in dec 85 and jan 86. Kac moody algebras lecture notes alexander kleshchev download bok. This is the long awaited followup to lie algebras, part i which covered a major part of the theory of kac moody algebras. Concerned with kac moody algebras, a particular class of infinitedimensional lie algebras, and their representations, this is the third revision of an important monograph. One of the distinguished features of infinite dimensional lie algebras is the modular. Each chapter begins with a motivating discussion and ends with a collection of exercises with. Integrable representations and the weyl group of a kac moody algebra.
Infinitedimensional lie algebras school of mathematics. The final classification of simple finitedimensional lie superalgebras is as follows section 4. An introduction progress in mathematics on free shipping on qualified orders. To every nitedimensional lie group see the denition below it is a special case of a continuous group all rotations around a xed center in r 3 gives an example one can assign a nitedimensional lie algebra also dened below. A new class of infinite dimensional simple lie algebras over a field with characteristic 0 are constructed. Let l ct, t1 be the ring of laurent polynomials in t, and set lb l oc 0. Projective unitary representations of infinitedimensional lie groups janssens, bas and neeb, karlhermann, kyoto journal of mathematics, 2019.
Infinite dimensional lie algebras of type l request pdf. The three preceding examples all give the same lie algebra structure. Finite and infinite dimensional lie algebras and applications in physics e. Universal enveloping algebra and the casimir operator. Cambridge core algebra infinitedimensional lie algebras by victor g. Part ii deals mainly with the representations and applications of lie algebras and contains many cross references to part i. Infinite dimensional lie algebras third edition infinite dimensional lie algebras third editionvictor g. In mathematics, an affine lie algebra is an infinitedimensional lie algebra that is constructed in a canonical fashion out of a finitedimensional simple lie algebra. In this paper we study the complete reducibility of representations of infinite dimensional lie algebras from the perspective of the representation theory of vertex algebras. Infinitedimensional lie algebras pdf free download epdf. This is an infinite dimensional lie algebra over c. Raina tata institute offundamentalresearch,india natasha rozhkovskaya kansasstateuniversity, usa worldscientific new jersey london singapore beijing shanghai hong kong taipei chennai. Modular invariant representations of infinitedimensional lie. Infinitedimensional lie algebras kindle edition by kac, victor g download it once and read it on your kindle device, pc, phones or tablets.
A conference on vertex algebras and related topics at rims, to appear. The infinitedimensional lie algebras could be useful in the construction of generalized newtoncartan theories gravity theories and. This is the third, substantially revised edition of this important monograph. Infinitedimensional lie algebras, theta functions and modular forms author links open overlay panel victor g kac dale h peterson. Constructing groups associated to infinitedimensional lie. Infinite lie algebras and theta functions 127 the affine lie algebra g associated to 1 may be constructed as follows 14,31, 7,181. Thence we can build a real formofthewittalgebraas x. Structure of a new class of nongraded infinite dimensional. Solitons and infinite dimensional lie algebras by michio jimbo and tetsuji miwa contents introduction 1. A particular wellunderstood class of infinitedimensional kacmoody algebras, the affine lie algebras, have found numerous applications throughout mathematics.
We prove a character formula for a large class of highest weight representations l. Use features like bookmarks, note taking and highlighting while reading infinitedimensional lie algebras. The book is concerned with kac moody algebras, a particular class of infinitedimensional lie algebras, and their representations. Each chapter begins with a motivating discussion and ends with a collection of exercises with hints to the more challenging problems. There are three valuable works on it, written by victor g kac. The witt algebra was a simple point of departure for infinite dimensional lie algebras. Frenkel, kac and wakimoto fkw conjectured that one can obtain a. Mathematical sciences research institute publications, vol. Examples will include certain direct limit lie algebras and, via automorphisms of order 3, all the exceptional lie algebras. An application of collapsing levels to the representation theory of affine vertex algebras. However, in nonzero characteristics, both semisimple and cartan type lie algebras have nontrivial deformations, as was shown by rudakov 1971 in. Affine lie algebras and tensor categories, 14 pages, proceedings of 10th cft seminar.
Contragredient lie algebras and lie algebras associated with a standard pentad sasano, nagatoshi, tsukuba journal of mathematics, 2018. The same is true for infinitedimensional classical lie algebras from the cartan series. Infinite dimensional lie algebras an introduction progress. Bombay lectures on highest weight representations of infinite dimensional lie algebras victor g. In this paper, we launch a program to describe and classify modular invariant representations of infinitedimensional lie algebras and superalgebras. Infinitedimensional lie groups and algebras in mathematical physics this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper we study the complete reducibility of representations of infinitedimensional lie algebras from the perspective of the representation theory of vertex algebras. Lectures on infinitedimensional lie algebra book pdf, epub ebook. Projective unitary representations of infinite dimensional lie groups janssens, bas and neeb, karlhermann, kyoto journal of mathematics, 2019. Infinite dimensionallie algebras second edition victorg. Classification and construction of semisimple lie algebras. The representation theory of affine lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. Lie algebras constructed with lie modules and their positively and negatively graded modules sasano, nagatoshi, osaka journal of mathematics, 2017. Infinite dimensional lie algebras occurring in algebraic geometry spring 2015 content of the course this course is set up as an introduction to the theory of conformal blocks wesszuminowitten theory, whose ultimate goal is described below. Lie superalgebras are a natural generalization of lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. The final classification of simple finite dimensional lie superalgebras is as follows section 4. It is based on courses given over a number of years at mit and in paris, and is sufficiently selfcontained and detailed to be used for graduate courses. Another application of this method is the chevalley type restriction theorem for simple finitedimensional lie superalgebras.
Continuing on, the main subjects of the book are the structure real and imaginary root systems of and the. Lie algebras with prescribed sl n decomposition this talk will describe lie algebras that have a speci c type of decomposition relative to an sl n subalgebra. This is the long awaited followup to lie algebras, part i which covered a major part of the theory of kac moody algebras, stressing primarily their mathematical structure. His brother boris katz is a principal research scientist at mit. Request pdf on jan 1, 2003, steven duplij and others published infinitedimensional lie algebra find, read and cite all the research you need on researchgate. On simplicity of certain infinite dimensional lie algebras. The book is concerned with kacmoody algebras, a particular class of. Introduction to finite and infinite dimensional lie. On complete reducibility for infinitedimensional lie algebras by maria gorelik and victor kac download pdf 510 kb. On complete reducibility for infinitedimensional lie algebras. Raina this book is a collection of a series of lectures given by prof. Infinite dimensional lie algebras occurring in algebraic. The theoretical part largely deals with the representation theory of lie algebras with a. Mathematical sciences research institute publications, vol 4.
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