000 05896cam a2200493Ii 4500
001 ocn948296975
003 OCoLC
005 20190328114815.0
006 m o d
007 cr cnu---unuuu
008 160429s2016 ne ob 001 0 eng d
040 _aN$T
_beng
_erda
_epn
_cN$T
_dN$T
_dIDEBK
_dOPELS
_dYDXCP
_dCDX
_dOCLCF
_dEBLCP
_dCOO
_dD6H
_dFEM
_dOCLCQ
_dU3W
_dCNCGM
_dOCLCQ
019 _a950464392
_a968077466
_a968995374
020 _a9780128046838
_qelectronic bk.
020 _a012804683X
_qelectronic bk.
020 _z9780128046753
020 _z0128046759
035 _a(OCoLC)948296975
_z(OCoLC)950464392
_z(OCoLC)968077466
_z(OCoLC)968995374
050 4 _aQA252.3
072 7 _aMAT
_x002040
_2bisacsh
082 0 4 _a512/.55
_223
100 1 _aSthanumoorthy, N.
_q(Neelacanta),
_d1945-
_eauthor.
245 1 0 _aIntroduction to finite and infinite dimensional lie (super)algebras /
_h[electronic resource]
_cN. Sthanumoorthy.
264 1 _aAmsterdam :
_bElsevier,
_c2016.
300 _a1 online resource
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_2rda
588 0 _aOnline resource; title from PDF title page (EBSCO, viewed May 3, 2016)
504 _aIncludes bibliographical references and index.
505 0 _aFront Cover; Introduction to Finite and Infinite Dimensional Lie (Super) algebras; Copyright; Dedication; Contents; About the author; Acknowledgement; Preface; Author Acknowledgements; Chapter 1: Finite-dimensional Lie algebras; 1.1 Basic definition of Lie algebras with examples and structure constants; A Lie algebra can also be defined starting from the definition of an algebra; Lie algebras of one, two, and three dimensions and their structure constants; 1.2 Subalgebras of Lie algebras and different classes of subalgebras of gl(n, C); 1.2.1 Different subalgebras of gl(n, C).
505 8 _aFour families of classical Lie algebras, namely, An, Bn, Cn, and Dn and their bases1.3 Ideals, quotient Lie algebras, derived sub Lie algebras, and direct sum; 1.4 Simple Lie algebras, semisimple Lie algebras, solvable and nilpotent Lie algebras; 1.5 Isomorphism theorems, Killing form, and some basic theorems; Examples for the matrix of the Killing form; 1.6 Derivation of Lie algebras; 1.7 Representations of Lie algebras and representations of sl(2,C); Representation of sl(2,C) in an (n + 1)-dimensional vector space.
505 8 _aGeneral theory of the representation of sl(2,C). Throughout this section G denotes sl(2,C)1.8 Rootspace decomposition of semisimple Lie algebras; Basic properties of root systems; Root space decomposition and properties of Killing form; 1.9 Root system in Euclidean spaces and root diagrams; 1.10 Coxeter graphs and Dynkin diagrams; 1.11 Cartan matrices, ranks, and dimensions of simple Lie algebras; Cartan matrices of classical simple Lie algebras; 1.12 Weyl groups and structure of Weyl groups of simple Lie algebras.
505 8 _a1.13 Root systems of classical simple Lie algebras and highest long and short roots1.14 Universal enveloping algebras of Lie algebras; The above definition can also be written as follows; The universal mapping property; 1.15 Representation theory of semisimple Lie algebras; 1.16 Construction of semisimple Lie algebras by generators and relations; 1.17 Cartan-Weyl basis; 1.18 Character of a finite-dimensional representation and Weyl dimension formula; 1.19 Lie algebras of vector fields; Some basic properties of Lie algebras of vector fields; Exercises; Chapter 2: Kac-Moody algebras.
505 8 _a2.1 Basic concepts in Kac-Moody algebrasHence for a symmetrizable Cartan matrix, one can give the following definition for Kac-Moody algebra; 2.2 Classification of finite, affine, hyperbolic, and extended-hyperbolic Kac-Moody algebras and their Dynkin diagrams; Properties of Dynkin diagrams; Dynkin diagrams for affine types; Properties of matrices of finite and affine types; For a GCM of affine type, Dynkin diagrams of A and At; Some properties of Dynkin diagrams of hyperbolic types; Some examples of Cartan matrices of hyperbolic types and their Dynkin diagrams.
520 _aLie 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.
650 0 _aLie algebras.
650 7 _aMATHEMATICS / Algebra / Intermediate
_2bisacsh
650 7 _aLie algebras.
_2fast
_0(OCoLC)fst00998125
655 4 _aElectronic books.
776 0 8 _iPrint version:
_aSthanumoorthy, Neelacanta.
_tIntroduction to Finite and Infinite Dimensional Lie (Super)algebras.
_dSan Diego : Elsevier Science, �2016
_z9780128046753
856 4 0 _3ScienceDirect
_uhttp://www.sciencedirect.com/science/book/9780128046753
999 _c247325
_d247325