Manchester Geometry Seminar 1999/2000
Manchester Algebra Seminar 1999/2000

Right-symmetric algebras satisfy the identity a·(b·c)-(a·b)·c = a·(c·b)-(a·c)·b. Example: the Witt algebra W_n (algebra of formal vector fields with n variables) is right-symmetric under multiplication u¶_i·v¶_j = v¶_j(u)¶_i. The author developed a cohomology theory for right-symmetric algebras. Connection between right-symmetric and Lie algebra cohomologies was established. It was used in calculation of "hidden" deformations and non-split extensions of four Cartan series of Lie algebras of vector fields. In particular, it was proved that:

• Lie algebras of divergence-free vector fields and Hamiltonian vector fields have new central extensions,
• Virasoro algebra has one more hidden central extension.

All necessary notions will be introduced in the talk.