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advanced_tools:group_theory:representation_theory:adjoint_representation
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Adjoint Representation
Intuitive
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.
Concrete
For a detailed discussion, see What’s so special about the adjoint representation of a Lie group? by J. Schwichtenberg
Diagram by Eduard Sackinger
Abstract
The motto in this section is: the higher the level of abstraction, the better.
Why is it interesting?
A 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 Lie algebra of the group!
The representation of each group where it acts on its own Lie algebra is called the adjoint representation.
advanced_tools/group_theory/representation_theory/adjoint_representation.1523803097.txt.gz · Last modified: 2018/04/15 14:38 (external edit)
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