Canonical endomorphism field on a Lie algebra

Details Canonical endomorphism field on a Lie algebra Canonical endomorphism field on a Lie algebra

2012-01-06

arxiv.org/abs/1201.1354v1

Journal of Generalized Lie Theory and Applications, Vol. 4 (2010), Article ID G100302, 15 pages

Physics

Mathematical Physics

18 pages

Scientific paper

10.4303/jglta/G100302

We show that every Lie algebra is equipped with a natural $(1,1)$-variant tensor field, the "canonical endomorphism field", naturally determined by the Lie structure, and satisfying a certain Nijenhuis bracket condition. This observation may be considered as complementary to the Kirillov-Kostant-Souriau theorem on symplectic geometry of coadjoint orbits. We show its relevance for classical mechanics, in particular for Lax equations. We show that the space of Lax vector fields is closed under Lie bracket and we introduce a new bracket for vector fields on a Lie algebra. This bracket defines a new Lie structure on the space of vector fields.

Affiliated with

Also associated with

No associations

Rating

Canonical endomorphism field on a Lie algebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Canonical endomorphism field on a Lie algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Canonical endomorphism field on a Lie algebra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-661762