Quantization, deformations, and new homological and categorical
methods in mathematical physics
n-Lie Structures, Hidden Deformations and Identities
(Institute of Mathematics Almaty)
Second cohomology groups for four Cartan series of Lie algebras of vector fields are calculated. We develop right-symmetric cohomology of algebras of vector fields. Some applications of cocyle constructions are given:
- The algebra of divergence-free vector fields on T2 has a 5-commutator.
- The Witt algebra W1 has 4-parametric right-symmetric deformations, but
only two of them can be prolongated to global deformation.
- The Witt algebra Wn has a (n2+2n-2)-commutator and it satisfies an identity of degree n2+2n-1.