Definition 4

Tag 0AA3, permanent. Cite it as [Bourbaki, Tag 0AA3].

Lie Groups and Lie Algebras, chapter III, § 3. Passage from a Lie group to its Lie algebra

Let G be a Lie group. A field of distributions on G is called left (resp. right) invariant if it is invariant under left (resp. right) translations of G.

In other words, a field of distributions $g \mapsto \Delta_g$ on $G$ is left invariant if

\Delta_{gg'} = \gamma(g) * \beta_{g'}

for

g, g'

G

, or again if

\Delta_{gg'} = \varepsilon_g * \Delta_{g'}

for

g, g'

G

. It is right invariant if

\Delta_{gg'} = \delta({g'}^{-1}) * \Delta_g

for

g, g'

G

, or again if:

\Delta_{gg'} = \Delta_g * \varepsilon_g,

for

g, g'

G

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Nothing.