Lie group
noun ·Rare ·Advanced level
Definitions
- 1 Any group that is a smooth manifold and whose group operations are differentiable.
"1994, Silvio Levy (translator), Albert S. Schwarz, Topology for Physicists, [1989, A. S. Shvarts, Kvantovaya teoriya polya i topologiya], Springer, 1996, 2nd Printing, page 233, Every connected Lie group is homotopically equivalent to its maximal compact subgroup. This reduces the study of the homotopy and homology of Lie groups to the compact case."
Synonyms
All synonymsExample
More examples"1994, Silvio Levy (translator), Albert S. Schwarz, Topology for Physicists, [1989, A. S. Shvarts, Kvantovaya teoriya polya i topologiya], Springer, 1996, 2nd Printing, page 233, Every connected Lie group is homotopically equivalent to its maximal compact subgroup. This reduces the study of the homotopy and homology of Lie groups to the compact case."
Etymology
Named for Norwegian mathematician Sophus Lie.