Generalized conformal realizations of Kac-Moody algebras

Details Generalized conformal realizations of Kac-Moody algebras Generalized conformal realizations of Kac-Moody algebras

2007-11-03

arxiv.org/abs/0711.0441v2

J.Math.Phys.50:013532,2009

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, v2: abstract and introduction rewritten, contents rearranged, former section 4 moved to an appendix

Scientific paper

10.1063/1.3063628

We present a construction which associates an infinite sequence of Kac-Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n=1, this reduces to the well known Kantor-Koecher-Tits construction. Our generalization utilizes a new relation between different generalized Jordan triple systems, together with their known connections to Jordan and Lie algebras. Applied to the Jordan algebra of hermitian 3x3 matrices over the division algebras R, C, H, O, the construction gives the exceptional Lie algebras f4, e6, e7, e8 for n=2. Moreover, we obtain their infinite-dimensional extensions for n greater or equal to 3. In the case of 2x2 matrices the resulting Lie algebras are of the form so(p+n,q+n) and the concomitant nonlinear realization generalizes the conformal transformations in a spacetime of signature (p,q).

Affiliated with

Also associated with

No associations

Rating

Generalized conformal realizations of Kac-Moody algebras 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 Generalized conformal realizations of Kac-Moody algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized conformal realizations of Kac-Moody algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-508005