Askar Dzhumadil'daev (Institute of Mathematics, Kazakhstan National Academy of Sciences)
askar@math.kz
Right-symmetric algebras satisfy the identity a·(b·c)-(a·b)·c = a·(c·b)-(a·c)·b. Example: the Witt algebra Wn (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:
All necessary notions will be introduced in the talk.