Lie group

Noun

Meaning

Lie group (plural Lie groups)

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

Source: en.wiktionary.org

Related terms

Lie algebra group of Lie type

Examples

A construction on Lie groups On an n-dimensional Lie group, Haar measure can be constructed easily as the measure induced by a left-invariant n-form. Source: Internet

As for classification, it can be shown that any connected Lie group with a given Lie algebra is isomorphic to the universal cover mod a discrete central subgroup. Source: Internet

Any Lie group gives rise to a Lie algebra. Source: Internet

Conversely, to any finite-dimensional Lie algebra over real or complex numbers, there is a corresponding connected Lie group unique up to covering ( Lie's third theorem ). Source: Internet

For example, an infinite-dimensional Lie algebra may or may not have a corresponding Lie group. Source: Internet

Constructions There are several standard ways to form new Lie groups from old ones: *The product of two Lie groups is a Lie group. Source: Internet

Close letter words and terms

lie down on the job lie down to sleep lie face downwards lie hid lie ideal lie in