A Lie algebra attached to a projective variety
Copyright policy )A Lie algebra attached to a projective variety
Each choice of a Kähler 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 Kähler 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, hyperkähler manifolds and flag varieties. We pay special attention to the cases where this leads to a Jordan algebra structure or a graded Frobenius algebra.
AMSTeX v2.1, 46 pages
- Indiana University United States
- Utrecht University Netherlands
- DePaul University United States
Local differential geometry of Hermitian and Kählerian structures, projective manifolds, 17B20, 14C30, 17C50 (Primary) 32J27, 14K10 (Secondary), Lie algebra, Grassmannians, Schubert varieties, flag manifolds, Mathematics - Algebraic Geometry, Landbouwwetenschappen, Wiskunde: algemeen, Kähler class, Natuurwetenschappen, Jordan structures associated with other structures, Transcendental methods, Hodge theory (algebro-geometric aspects), complex cohomology, FOS: Mathematics, Wiskunde en Informatica (WIIN), Homological methods in Lie (super)algebras, Algebraic Geometry (math.AG), Mathematics, Simple, semisimple, reductive (super)algebras, de Rham cohomology and algebraic geometry
Local differential geometry of Hermitian and Kählerian structures, projective manifolds, 17B20, 14C30, 17C50 (Primary) 32J27, 14K10 (Secondary), Lie algebra, Grassmannians, Schubert varieties, flag manifolds, Mathematics - Algebraic Geometry, Landbouwwetenschappen, Wiskunde: algemeen, Kähler class, Natuurwetenschappen, Jordan structures associated with other structures, Transcendental methods, Hodge theory (algebro-geometric aspects), complex cohomology, FOS: Mathematics, Wiskunde en Informatica (WIIN), Homological methods in Lie (super)algebras, Algebraic Geometry (math.AG), Mathematics, Simple, semisimple, reductive (super)algebras, de Rham cohomology and algebraic geometry
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