Revision #196 → #1358 · back to history
addedLie algebra10c1c4916ac5
addedCommutator Lie algebra from an associative algebra0460518f321a
addedCross product Lie algebra on R^36800bc596540
addedFundamental example: linear maps of a vector space7359f01f0832
addedLie algebra (axioms)0b64e89fcda2
addedAnticommutativity from bilinearity and alternatinga56be8d51981
addedAnticommutativity implies alternating in char ≠ 27ae65d41d269
addedJacobi identity as Leibniz rule (derivation property)5ecdc88c1082
addedDimension of a Lie algebrafb399db915d8
addedGenerators of a Lie algebra50f3125bbf66
addedAbelian Lie algebra75754362a8ad
addedOne-dimensional Lie algebras are abelian45870b4fb6b2
addedCommutator Lie bracket on an associative algebrabbb05c21f159
addedEndomorphism Lie algebra gl(V)d03a74dee62a
addedGeneral linear Lie algebra gl_n(F)979c7fc695f9
addedgl_n(R) as Lie algebra of GL(n,R)4d33d00bd84a
addedLie subalgebrab5c48b37bc10
addedIdeal of a Lie algebraf12c88c88d0e
addedLie algebra homomorphism16ff957e7f78
addedIsomorphism of Lie algebras49974a67a842
addedFirst isomorphism theorem for Lie algebrasc1ce2502cdbd
addedCommuting elementsaf507621cc15
addedCentralizer and centerfcdfa6cd30e3
addedNormalizer subalgebrac056b8dcbde0
addedDiagonal matrices as abelian subalgebradc587124a956
addedOne-dimensional subspaces are abelian subalgebras25b6389772d0
addedProduct Lie algebra0baa0704dc99
addedSemidirect product of Lie algebras7c78d93f8831
addedDerivation of an algebrae685d4eaed3f
addedDerivations form a Lie algebra120c227f1d21
addedLie algebra of vector fields8a415ac948bb
addedInner derivation2ab83ae03f6e
addedOuter derivations520c1df55ea4
addedDerivations of semisimple Lie algebras are inner9b6b01d18fdd
addedMatrix group and its Lie algebra50f9d0c4a6af
addedRecovering Lie group via matrix exponentiale5d081ce5501
addedSpecial linear group and sl_n663a1192b40c
addedOrthogonal group and so_nc04d2955158c
addedComplex orthogonal group and Lie algebra5af56b8d32fe
addedUnitary group and u_n398ebc521945
addedSpecial unitary group and su_n7e531715f857
addedSymplectic group and symplectic Lie algebra4c13b5d9c70f
addedClassical Lie algebrasfccb2823a3f1
addedUnique nonabelian 2-dimensional Lie algebrabdf1cac582ce
addedAffine group as matricesfdca439f424b
addedHeisenberg algebra80fdc35ad088
addedHeisenberg algebra is nilpotent1a5d386b5af9
addedso(3) as skew-symmetric matrices5023af286b8d
addedso(3) is simple5b3a268d8e8f
addedsl(2) of trace-zero 2×2 matrices830b0f94b0ff
addedsl(2) is simple801769753041
addedsl(2,C) is the complexification of su(2)ece9dd7dc4e3
addedVector fields as infinite-dimensional Lie algebra55df28bf1528
addedKac–Moody algebrasea3f591e86dd
addedMoyal algebra1c4bab0ed137
addedVirasoro algebraeaa30a8ab4f1
addedFree Lie algebra25b00aeb729c
addedRepresentation of a Lie algebra834c766e1f11
addedFaithful representation78989aaed142
addedAdo's theorem5b37684d5c2a
addedAdjoint representationb10e67f42007
addedWeyl's complete reducibility theoremdbfff4f86aa2
addedUniversal enveloping algebrab50b8926116e
addedPoincaré–Birkhoff–Witt theoremb8a4a38a12e7
addedClassification of abelian Lie algebras1c20b2170255
addedCommutator (derived) subalgebrab3038acac94d
addedNilpotent Lie algebra30b39ba0426c
addedEngel's theoreme1e1a50f1816
addedSolvable Lie algebraf6dfe98bebb7
addedRadical of a Lie algebrac003eff221fc
addedSimple Lie algebra2fcdeee0befe
addedSemisimple Lie algebrac3257e69a498
addedSemisimple iff product of simple Lie algebras3271e59a2d59
addedsl_n is simple3f8b7d0d9490
addedSemisimplicity of representations of semisimple Lie algebras4ff09b4d6486
addedReductive Lie algebrad0dd1e860fc8
addedStructure of reductive Lie algebrasf5f7c0f896d2
addedKilling forme1831660aeee
addedCartan's criterion for semisimplicity3ebe931b942d
addedLevi decomposition4190e56965b0
addedKilling–Cartan classification of simple Lie algebrasf12a7e0a6a23
addedLie's third theorem490e06f3b8d9
addedEquivalence of categories for simply connected Lie groupsd8566d6dbf95
addedConnected Lie group as universal cover mod discrete center7d8c98620e69
addedReal form of a complex Lie algebra1c90b45ed835
addedSplit form83d83b253336
addedCompact form43618bb29c29
addedGraded Lie algebra9296314b909c
addedDifferential graded Lie algebrada09606ad30f
addedHomotopy groups as a graded Lie algebrab25c99c9f231
addedLie algebra over a commutative ring (Lie ring)463944475cf7
addedLie ring from a group filtration9dbd27abd68d
addedLie ring of dihedral group of order 8d32c91145b66
addedCategory-theoretic definition of Lie algebra22339d6d2fc5