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Lie group

In mathematics, a Lie group (pronounced /liː/ Lee) is a group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.

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Overview

History

Definitions and examples

More examples of Lie groups

Basic concepts

Representations

Classification

Infinite-dimensional Lie groups

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Map overview Semantic statistics

Lie group

Nodes260
Edges259
Triples189
Avg. degree1.99
Density0.007692
Components1

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Lie group

Top relations

related to Additional examples · 17
Lie group → Along, E6, E7, E8, F4, G2, It, Lie, Minkowski, Omega, Sp, SU, The, The Heisenberg, The Lorentz, The Poincaré, Topologically
related to Classification · 14
Lie group → An, Bn, But, Cn, Dn, E8, Euclidean, Examples, Hence, It, Lie, The, The Lie, What
related to The Lie algebra associated with a Lie group · 14
Lie group → AAT, AB, BA, Before, For, GL, If, In, Informally, Lie, Rn, The, The Lie, To
related to Matrix Lie groups · 13
Lie group → Any, GL, Hall, Let GL, Lie, Restricting, Rossmann, Since, SL, SO, Stillwell, SU, The
related to Related concepts · 13
Lie group → Gleason, Hilbert, Hilbert's, If, In, It, Lie, Montgomery, Similarly, SL, Smith, The, Zippin
related to Representations · 13
Lie group → Assume, Consider, Hamiltonian, Hermann Weyl, In, Lie, One, Rather, Schrödinger, SO, The, These, This
related to Infinite-dimensional Lie groups · 11
Lie group → Banach, Euclidean, For, However, In, Instead, It, Lie, On, That, The
related to Topological definition · 11
Lie group → Conversely, Given, GL, Hausdorff, Hence, Lie, Lie's, One, Precisely, Showing, Then
related to First examples · 9
Lie group → Addition, GL, It, Lie, SO, The, This, Thus, Using
is a · 8
Lie group → example of a gauge group, group object in the category of smooth manifolds, group that is also a finite-dimensional real smooth manifold, Lie algebra under the Lie bracket of vector fields.Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tan…, Lie group, open normal subgroup, semidirect product of a solvable normal subgroup and a semisimple subgroup.Connected compact Lie groups are all known, simply connected Lie group

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Important terminology

lie group groups displaystyle algebra connected subgroup theory example one manifold mathbb matrices real map simple space algebras smooth representations

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Lie groupis agroup that is also a finite-dimensional real smooth manifold0.90text
Lie groupis agroup object in the category of smooth manifolds0.90text
Lie groupis aLie group0.90text
Lie groupis aLie algebra under the Lie bracket of vector fields.Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tan…0.90text
Lie groupis asemidirect product of a solvable normal subgroup and a semisimple subgroup.Connected compact Lie groups are all known0.90text
Lie groupis aopen normal subgroup0.90text
Lie groupis asimply connected Lie group0.90text
Lie groupis aexample of a gauge group0.90text
Lie grouprelated to Additional examplesThe0.60section
Lie grouprelated to Additional examplesSU0.60section
Lie grouprelated to Additional examplesTopologically0.60section
Lie grouprelated to Additional examplesThe Heisenberg0.60section

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