✎ Adjoint Representation [The Physics Travel Guide]

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====== Adjoint Representation ======

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
</note>
  
<tabbox Concrete> 
For a detailed discussion, see [[http://jakobschwichtenberg.com/adjoint-representation/|What’s so special about the adjoint representation of a Lie group?]] by J. Schwichtenberg

[{{ :advanced_tools:group_theory:representation_theory:adjointaction.png?nolink |Diagram by Eduard Sackinger}}]
 
<tabbox Abstract>

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

A [[advanced_tools:group_theory:representation_theory|representation]] is a map that maps each element of the set of abstract groups element to a matrix that acts on a vector space. A confusing point here is: If we can study the representation of any group on any vector space, where should we start?

Luckily there comes exactly only distinguished vector space automatically with each Lie group: the [[advanced_tools:group_theory:lie_algebras|Lie algebra]] of the group!

The representation of each group where it acts on its own Lie algebra is called the adjoint representation.

</tabbox>

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