Symmetry: Representation Theory and Its Applications by Roger Howe Markus Hunziker & Jeb F. Willenbring

Author:Roger Howe, Markus Hunziker & Jeb F. Willenbring
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(2.1c)

The differential (in the target variable) of this action is an action of G on by Lie algebra automorphisms

(2.1d)

This differential of this action of G is a Lie algebra homomorphism

(2.1e)

Analogous notation will be used for arbitrary real Lie groups. The kernel of the adjoint action of G on G or on is the center Z(G):

(2.1f)

So far all of this applies to arbitrary connected Lie groups G. We will also have occasion to use the existence of a nondegenerate symmetric bilinear form B on , with the invariance properties

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