A Lie algebra attached to a projective variety

Details A Lie algebra attached to a projective variety A Lie algebra attached to a projective variety

1996-04-24

arxiv.org/abs/alg-geom/9604014v1

Mathematics

Algebraic Geometry

AMSTeX v2.1, 46 pages

Scientific paper

10.1007/s002220050166

Each choice of a K\"ahler class on a compact complex manifold defines an action of the Lie algebra $\slt$ on its total complex cohomology. If a nonempty set of such K\"ahler classes is given, then we prove that the corresponding $\slt$-copies generate a semisimple Lie algebra. We investigate the formal properties of the resulting representation and we work things out explicitly in the case of complex tori, hyperk\"ahler manifolds and flag varieties. We pay special attention to the cases where this leads to a Jordan algebra structure or a graded Frobenius algebra.

Affiliated with

Also associated with

No associations

Rating

A Lie algebra attached to a projective variety 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 A Lie algebra attached to a projective variety, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Lie algebra attached to a projective variety will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-551236