Meaning of Lie group | Babel Free

Definitions

Any group that is a smooth manifold and whose group operations are differentiable.

Equivalents

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.”

“A Lie⟳ group is a manifold on which the group manipulations, product and inverse, arc defined. Lie⟳ groups play⟳ an extremely important role in the theory of fibre bundles and also find⟳ vast applications in physics.”

“As is well known, in finite dimensions each Lie⟳ group is, at least locally near the identity, completely described by its Lie⟳ algebra.”

CEFR level