About: Glossary of Lie groups and Lie algebras

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This is a glossary for the terminology applied in the mathematical theories of Lie groups and Lie algebras. For the topics in the representation theory of Lie groups and Lie algebras, see Glossary of representation theory. Because of the lack of other options, the glossary also includes some generalizations such as quantum group. Notations: Throughout the glossary, denotes the inner product of a Euclidean space E and denotes the rescaled inner product

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rdfs:label	Glossary of Lie groups and Lie algebras (en)
rdfs:comment	This is a glossary for the terminology applied in the mathematical theories of Lie groups and Lie algebras. For the topics in the representation theory of Lie groups and Lie algebras, see Glossary of representation theory. Because of the lack of other options, the glossary also includes some generalizations such as quantum group. Notations: Throughout the glossary, denotes the inner product of a Euclidean space E and denotes the rescaled inner product (en)
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dcterms:subject	Lie algebras Glossaries of mathematics
Wikipage page ID	62157107 (xsd:integer)
Wikipage revision ID	1106589544 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Carl Gustav Jacob Jacobi Cartan criterion for solvability En (Lie algebra) Coroot Basis (linear algebra) Borel subalgebra Algebra over a field Algebraically closed field E7 (mathematics) Index of a Lie algebra Invariant convex cone Iwasawa decomposition Jacobi identity Levi decomposition Lie's theorem Lie group Lie group–Lie algebra correspondence (B, N) pair Lie algebras Compact Lie group Complex reflection group Chevalley basis Generalized Kac–Moody algebra Generalized Verma module Quantized enveloping algebra Claude Chevalley Clebsch–Gordan coefficients Eigenvector Glossary of representation theory Glossaries of mathematics Traceless Alternating map Lie algebra Lie algebra extension Lie groups Analytic subgroup Claudio Procesi Élie Cartan Harish-Chandra homomorphism Maximal compact subgroup Ado's theorem Toral Lie algebra Wilhelm Killing Casimir invariant G2 (mathematics) Karin Erdmann Nilpotent cone Nilpotent ideal Affine Lie algebra E6 (mathematics) E8 (mathematics) Finite field Nilpotent Lie algebra Nilpotent element Glossary Kac–Moody algebra Radical of a Lie algebra Regular element of a Lie algebra Harish-Chandra Harold Scott MacDonald Coxeter Hermann Weyl Adjoint representation of a Lie algebra Adjoint representation of a Lie group Coxeter group Dynkin diagrams Reductive Lie algebra Simple Lie group Armand Borel Abelian Lie algebra Abelian Lie group Chevalley group Killing form Langlands decomposition Maximal torus Reductive group Reflection group Automorphism of a Lie algebra Borel subgroup Sophus Lie Group analysis of differential equations Iff Inner product Bruhat decomposition Nathan Jacobson Cartan's criterion Cartan decomposition Cartan matrix Cartan subalgebra Cartan subgroup Semisimple Lie group

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