東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back to Search results for [ null ]

Switch To: Labeled | MARC Mode | ISBD

Introduction to finite and infinite ...

Sthanumoorthy, N. (1945-)

Linked to FindBook

Google Book

Amazon

博客來

Introduction to finite and infinite dimensional lie (super)algebras /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Introduction to finite and infinite dimensional lie (super)algebras // N. Sthanumoorthy.
Author:	Sthanumoorthy, N.
Description:	1 online resource
[NT 15003449]:	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).
[NT 15003449]:	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.
[NT 15003449]:	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.
[NT 15003449]:	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.
[NT 15003449]:	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.
Subject:	Lie algebras. -
Online resource:	https://www.sciencedirect.com/science/book/9780128046753
ISBN:	9780128046838

Introduction to finite and infinite dimensional lie (super)algebras /
Sthanumoorthy, N.1945-

Introduction to finite and infinite dimensional lie (super)algebras /N. Sthanumoorthy. - 1 online resource

Includes bibliographical references and index.

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).

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.

ISBN: 9780128046838Subjects--Topical Terms:

526115
Lie algebras.
Index Terms--Genre/Form:

542853
Electronic books.

LC Class. No.: QA252.3

Dewey Class. No.: 512/.55

Introduction to finite and infinite dimensional lie (super)algebras /
LDR:05206nmm a2200349 i 4500 001 2181989
006 m o d
007 cr cnu---unuuu
008 191128s2016 ne ob 001 0 eng d
020 $a 9780128046838 $q (electronic bk.)
020 $a 012804683X $q (electronic bk.)
020 $a 9780128046753
020 $a 0128046759
035 $a (OCoLC)948296975 $z (OCoLC)950464392 $z (OCoLC)968077466 $z (OCoLC)968995374 $z (OCoLC)1105188388 $z (OCoLC)1105570842
035 $a els19100113
040 $a N$T $b eng $e rda $e pn $c N$T $d N$T $d IDEBK $d OPELS $d YDXCP $d CDX $d OCLCF $d EBLCP $d COO $d D6H $d FEM $d OCLCQ $d U3W $d CNCGM $d OCLCQ $d LQU
041 0 $a eng
050 4 $a QA252.3
082 0 4 $a 512/.55 $2 23
100 1 $a Sthanumoorthy, N. $q (Neelacanta), $d 1945- $e author. $3 3389843
245 1 0 $a Introduction to finite and infinite dimensional lie (super)algebras / $c N. Sthanumoorthy.
264 1 $a Amsterdam : $b Academic Press, $c 2016.
300 $a 1 online resource
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
504 $a Includes bibliographical references and index.
505 0 $a 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 $a 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 $a 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 $a 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 $a 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 $a 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 $a Lie algebras. $3 526115
655 4 $a Electronic books. $2 lcsh $3 542853
856 4 0 $u https://www.sciencedirect.com/science/book/9780128046753