Introduction to finite and infinite dimensional lie (super)algebras / (Record no. 247325)
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| fixed length control field | 05896cam a2200493Ii 4500 |
| 001 - CONTROL NUMBER | |
| control field | ocn948296975 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20190328114815.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu---unuuu |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 160429s2016 ne ob 001 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | N$T |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | N$T |
| Modifying agency | N$T |
| -- | IDEBK |
| -- | OPELS |
| -- | YDXCP |
| -- | CDX |
| -- | OCLCF |
| -- | EBLCP |
| -- | COO |
| -- | D6H |
| -- | FEM |
| -- | OCLCQ |
| -- | U3W |
| -- | CNCGM |
| -- | OCLCQ |
| 019 ## - | |
| -- | 950464392 |
| -- | 968077466 |
| -- | 968995374 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780128046838 |
| Qualifying information | electronic bk. |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 012804683X |
| Qualifying information | electronic bk. |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780128046753 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 0128046759 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)948296975 |
| Canceled/invalid control number | (OCoLC)950464392 |
| -- | (OCoLC)968077466 |
| -- | (OCoLC)968995374 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA252.3 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 002040 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512/.55 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Sthanumoorthy, N. |
| Fuller form of name | (Neelacanta), |
| Dates associated with a name | 1945- |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Introduction to finite and infinite dimensional lie (super)algebras / |
| Medium | [electronic resource] |
| Statement of responsibility, etc. | N. Sthanumoorthy. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Amsterdam : |
| Name of producer, publisher, distributor, manufacturer | Elsevier, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2016. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Source | rda |
| 588 0# - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Online resource; title from PDF title page (EBSCO, viewed May 3, 2016) |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes bibliographical references and index. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Front 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# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Four 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# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | General 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# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1.13 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# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 2.1 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 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Lie algebras. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | MATHEMATICS / Algebra / Intermediate |
| Source of heading or term | bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Lie algebras. |
| Source of heading or term | fast |
| Authority record control number | (OCoLC)fst00998125 |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Sthanumoorthy, Neelacanta. |
| Title | Introduction to Finite and Infinite Dimensional Lie (Super)algebras. |
| Place, publisher, and date of publication | San Diego : Elsevier Science, �2016 |
| International Standard Book Number | 9780128046753 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | ScienceDirect |
| Uniform Resource Identifier | http://www.sciencedirect.com/science/book/9780128046753 |
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