Jacobi identity interpretations
The Jacobi identity in a Lie algebra has various interpretations
that are more transparent, whence easier to remember, than the usual form
One is the fact that the adjoint representation
11Here, “” means the space o
endomorphisms
of , viewed as a vector space, with Lie
bracket on being commutator
.
really is a representation
. Yet another way to formulate the identity
is
i.e., is a derivation on for all .
Title | Jacobi identity interpretations |
---|---|
Canonical name | JacobiIdentityInterpretations |
Date of creation | 2013-03-22 13:03:42 |
Last modified on | 2013-03-22 13:03:42 |
Owner | rspuzio (6075) |
Last modified by | rspuzio (6075) |
Numerical id | 8 |
Author | rspuzio (6075) |
Entry type | Definition |
Classification | msc 17B99 |