Minimal identity for differential operators and right-symmetric cohomology
by
A.S. Dzhumadil'daev
Institut Mittag-Leffler, Auravagen 17, Djursholm, S-18262, Sweden

An algebra with identity a o (b o c)-(a o b) o c=a o (c o b)-(a o c) o b is called right-symmetric. Example: Derivation algebra of Laurent power series under multiplication u d_i o v d_j = v d_j(u) d_i is right-symmetric (here d_i is partial derivation on x_i.). Its Lie algebra is Witt algebra W_n. Cohomology theory for right-symmetric algebras is developed. Applications of this theory in consideration of deformations, central extensions of vector fields Lie algebras are given. In particular, the following minimal identities for right-symmetric Witt algebras W_n are obtained. Left multiplication operators satisfy right polynomial identity of degree 2n and right multiplication operators satisfy left polynomial identity of degree n²+2n-1, n > 1.

Date received: February 15, 1999