isotropy representation
Let be a Lie algebra, and a subalgebra
. The
isotropy representation of relative to is the naturally
defined action of on the quotient vector space .
Here is a synopsis of the technical details. As is customary, we will use
to denote the coset elements of .
Let be given. Since is invariant with respect to
, the adjoint action factors through the quotient to
give a well defined endomorphism of . The action is given
by
This is the action alluded to in the first paragraph.
Title | isotropy representation |
---|---|
Canonical name | IsotropyRepresentation |
Date of creation | 2013-03-22 12:42:28 |
Last modified on | 2013-03-22 12:42:28 |
Owner | rmilson (146) |
Last modified by | rmilson (146) |
Numerical id | 6 |
Author | rmilson (146) |
Entry type | Definition |
Classification | msc 17B10 |
Related topic | AdjointRepresentation |