| Description |
1 online resource (408 pages) |
| Series |
De Gruyter studies in mathematical physics, 2194-3532 ; volume 35 |
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De Gruyter studies in mathematical physics.
|
| Contents |
1 Introduction ; 1.1 Symmetries ; 1.2 Invariant Differential Operators ; 1.3 Sketch of Procedure ; 1.4 Organization of the Book ; 2 Lie Algebras and Groups ; 2.1 Generalities on Lie Algebras ; 2.1.1 Lie Algebras ; 2.1.2 Subalgebras, Ideals, and Factor-Algebras |
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2.1.3 Representations 2.1.4 Solvable Lie Algebras ; 2.1.5 Nilpotent Lie Algebras ; 2.1.6 Semisimple Lie Algebras ; 2.1.7 Examples ; 2.2 Elements of Group Theory ; 2.2.1 Definition of a Group ; 2.2.2 Group Actions ; 2.2.3 Subgroups and Factor-Groups ; 2.2.4 Homomorphisms |
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2.2.5 Direct and Semidirect Products of Groups 2.3 Structure of Semisimple Lie Algebras ; 2.3.1 Cartan Subalgebra ; 2.3.2 Lemmas on Root Systems ; 2.3.3 Weyl Group ; 2.3.4 Cartan Matrix ; 2.4 Classification of Kac-Moody Algebras ; 2.5 Realization of Semisimple Lie Algebras |
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2.5.1 Special Linear Algebra 2.5.2 Odd Orthogonal Lie Algebra ; 2.5.3 Symplectic Lie Algebra ; 2.5.4 Even Orthogonal Lie Algebra ; 2.5.5 Exceptional Lie Algebra G2 ; 2.5.6 Exceptional Lie Algebra F4 ; 2.5.7 Exceptional Lie Algebras El ; 2.6 Realization of Affine Kac-Moody Algebras |
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2.6.1 Realization of Affine Type 1 Kac-Moody Algebras 2.6.2 Realization of Affine Type 2 and 3 Kac-Moody Algebras ; 2.6.3 Root System for the Algebras AFF 2 & 3 ; 2.7 Chevalley Generators, Serre Relations, and Cartan-Weyl Basis ; 2.8 Highest Weight Representations of Kac-Moody Algebras |
| Summary |
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory |
| Bibliography |
Includes bibliographical references (pages 375-401) and index |
| Notes |
2.9 Verma Modules |
|
Online resource; title from PDF title page (De Gruyter, viewed October 17, 2016) |
| Subject |
Semisimple Lie groups.
|
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Lie algebras.
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MATHEMATICS -- Algebra -- Intermediate.
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Lie algebras
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Semisimple Lie groups
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| Genre/Form |
Mathematics; Physics
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| Form |
Electronic book
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| ISBN |
9783110427646 |
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3110427648 |
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9783110427806 |
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311042780X |
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