Vipul at 00:25, 7 January 2012

2012-01-07T00:25:48Z

← Older revision		Revision as of 00:25, 7 January 2012
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	where <math>\operatorname{Ad}</math> denotes the [[adjoint action of Lie group on Lie algebra]].		where <math>\operatorname{Ad}</math> denotes the [[adjoint action of Lie group on Lie algebra]].

			===Statement for a linear Lie group===

			For a [[linear Lie group]], the statement reduces to [[matrix exponential commutes with conjugation]].

Vipul: Created page with "==Statement== ===Statement for a real Lie group=== Suppose $G$ is a real Lie group and $\mathfrak{g}$ is its [[Lie algebra of a real Lie group|Lie ..."

2012-01-07T00:24:38Z

Created page with "==Statement== ===Statement for a real Lie group=== Suppose <math>G</math> is a real Lie group and <math>\mathfrak{g}</math> is its [[Lie algebra of a real Lie group|Lie ..."

New page

==Statement==

===Statement for a real Lie group===

Suppose <math>G</math> is a [[real Lie group]] and <math>\mathfrak{g}</math> is its [[Lie algebra of a real Lie group|Lie algebra]]. For <math>g \in G</math> and <math>x \in \mathfrak{g}</math>, the following is true:

<math>\exp(\operatorname{Ad}(g)(x)) = g\exp(x)g^{-1}</math>

where <math>\operatorname{Ad}</math> denotes the [[adjoint action of Lie group on Lie algebra]].

Exponential map commutes with adjoint action - Revision history

Vipul at 00:25, 7 January 2012

Vipul: Created page with "==Statement== ===Statement for a real Lie group=== Suppose G is a real Lie group and \mathfrak{g} is its [[Lie algebra of a real Lie group|Lie ..."

Vipul: Created page with "==Statement== ===Statement for a real Lie group=== Suppose $G$ is a real Lie group and $\mathfrak{g}$ is its [[Lie algebra of a real Lie group|Lie ..."