Concept information
Terme préférentiel
Lie group
Définition(s)
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In mathematics, a Lie group is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additional properties it must have to be thought of as a "transformation" in the abstract sense, for instance multiplication and the taking of inverses (division), or equivalently, the concept of addition and the taking of inverses (subtraction). Combining these two ideas, one obtains a continuous group where multiplying points and their inverses are continuous. If the multiplication and taking of inverses are smooth (differentiable) as well, one obtains a Lie group.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Lie_group)
Concept(s) générique(s)
Concept(s) spécifique(s)
- affine group
- algebraic torus
- automorphic form
- Baker-Campbell-Hausdorff formula
- Bruhat decomposition
- Carnot group
- Cartan decomposition
- circle group
- closed-subgroup theorem
- complex Lie group
- covering group
- Darboux derivative
- Dunkl operator
- Einstein group
- exponential map
- Freudenthal magic square
- fundamental representation
- fundamental vector field
- general linear group
- group contraction
- Heisenberg group
- Hilbert's fifth problem
- Hitchin integrable system
- homogeneous space
- improper rotation
- indefinite orthogonal group
- infinitesimal transformation
- invariant convex cone
- Iwasawa decomposition
- Jacobi group
- Killing form
- Klein geometry
- Kleinian group
- Laguerre transformation
- Lie groupoid
- Lie's third theorem
- Lorentz group
- matrix exponential
- Maurer-Cartan form
- maximal compact subgroup
- maximal torus
- one-parameter subgroup
- orthogonal group
- ping-pong lemma
- pin group
- Poincaré group
- Poisson-Lie group
- polar decomposition
- projective linear group
- projective orthogonal group
- projective unitary group
- pseudogroup
- real form
- reductive group
- representation of a Lie group
- representation ring
- root system
- Schrödinger group
- special linear group
- special linear Lie algebra
- special unitary group
- spin group
- spin tensor
- symmetric cone
- symplectic group
- Trombi-Varadarajan theorem
- unitary group
- Virasoro group
- Vogel plane
- Wess-Zumino-Witten model
- Weyl group
Traductions
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français
URI
http://data.loterre.fr/ark:/67375/PSR-RMQ1RP9W-P
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