Statements (57)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Lie group
|
| gptkbp:hasExhibition |
gptkb:SO(n)
gptkb:Sp(n) O(n) SU(n) E_8 F_4 G_2 U(n) Spin(n) T^n |
| gptkbp:hasSpecialty |
compactness
connectedness finite-dimensional group structure smooth manifold abelian if and only if it is isomorphic to a torus finite center |
| https://www.w3.org/2000/01/rdf-schema#label |
compact Lie group
|
| gptkbp:isCharacterizedBy |
Haar measure exists
Lie algebra is semisimple closed subgroup of GL(n, C) finite number of irreducible representations |
| gptkbp:isRelatedTo |
representation theory
Riemannian manifold homogeneous space topological group topological invariance Lie algebra representation symmetry group |
| gptkbp:isUsedIn |
cryptography
string theory theoretical physics algebraic geometry differential geometry computer graphics data analysis machine learning mathematical physics number theory robotics algebraic topology category theory homotopy theory signal processing mathematical logic network theory statistical mechanics functional analysis control theory dynamical systems symmetry analysis topological quantum field theory representation theory of groups combinatorial topology quantum_field_theory quantum_mechanics |