A Lie algebra attached to a projective variety |
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| Authors: | Eduard Looijenga Valery A Lunts |
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| Institution: | (1) Faculteit Wiskunde en Informatica, Universiteit Utrecht, PO Box 80.010, 3508 TA Utrecht, The Netherlands (e-mail: looijeng math.ruu.nl), NL;(2) Department of Mathematics, Indiana University, Bloomington, IN 47405, USA (e-mail: vlunts@ucs.indiana.edu), IN |
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| Abstract: | Abstract. Each choice of a K?hler class on a compact complex manifold defines an action of the Lie algebra sl(2) on its total complex cohomology. If a nonempty set of such K?hler classes is given, then we prove that the corresponding
sl(2)-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?hler manifolds and flag varieties. We pay special attention
to the cases where this leads to a Jordan algebra structure or a graded Frobenius algebra.
Oblatum 21-V-1996 & 15-X-1996 |
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