Revision #949 → #1650 · back to history
addedUniversal enveloping algebra (informal)e27d99e4ed7f
addedIdentification with left-invariant differential operatorsf86af6cc4f7c
addedUniversal enveloping algebra as largest embedding801602344f52
addedU(g) via generators and relations3f5c39a64be6
addedUniversal enveloping algebra of sl(2,C)46768e7588ac
addedPBW basis spans U(g) (preview)5dad205518dd
addedFormal definition of U(g) as a quotient063cf150569d
addedU for Lie superalgebras0ee6974adba8
addedGerstenhaber algebra via exterior productfe1d1f6b6339
addedUniversal property of U(g)02ac0cc12702
addedPoincaré–Birkhoff–Witt theorem (basis form)877d4358cd7d
addedPBW: U(g) and symmetric algebra are isomorphic vector spaces793ed4ea9184
addedPBW theorem (coordinate-free)554d9de1d299
addedJordan algebra construction yields exterior algebra71de074ca3db
addedLeft-invariant differential operators isomorphic to U(g)16ac15aa5f9d
addedAlgebra of symbols74cdf7571480
addedHeisenberg algebra and Weyl algebra (Moyal product)00f749f145d0
addedRepresentations of g correspond to U(g)-modules6e542e4037d0
addedKronecker product isomorphism385a74759caa
addedU of free Lie algebra is free associative algebra77c43eddbf40
addedCasimir operators as basis of center15f9ce1f5b42
addedQuadratic Casimir operator99d3a54f9975
addedNumber of independent Casimirs equals rank84336cdb501c
addedCasimir for SO(3): squared angular momentum91a3a76c07cf
addedQuadratic Casimir as Laplacian on Riemannian manifoldsccc966192031
addedAbelian Lie algebra: U(g) is polynomial algebraac2d75b32e43
addedLie group case: U(g) as left-invariant differential operators14864b944c48
addedU(g) as convolution algebra of distributions at identity3f04cc3998ee
addedWeyl algebra from Heisenberg Lie algebra3fc258dd1728
addedU(g) is a filtered quadratic algebra8b8db32a81d8
addedGelfand–Naimark for commutative Hopf algebrasfa519f748cbe