Noncompact Semisimple Lie Algebras and Groups /

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....

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Dobrev, V. K. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin/Boston : De Gruyter, 2016.
Colección:De Gruyter studies in mathematical physics.
Temas:
Semisimple Lie groups.
Lie algebras.
Groupes de Lie semi-simples.
Algèbres de Lie.
MATHEMATICS > Algebra > Intermediate.
Lie algebras
Semisimple Lie groups
Mathematics; Physics.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.

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