1,466 research outputs found
Recommended from our members
Computability Theory
Computability is one of the fundamental notions of mathematics, trying to capture the effective content of mathematics. Starting from Gödel’s Incompleteness Theorem, it has now blossomed into a rich area with strong connections with other areas of mathematical logic as well as algebra and theoretical computer science
A Lie algebra attached to a projective variety
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.Comment: AMSTeX v2.1, 46 page
A Lie algebra attached to a projective variety
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.Comment: AMSTeX v2.1, 46 page
- …