Minimal identities for right-symmetric algebras

An algebra A with multiplication A x A --> A, (a, b) --> a o b, is called right symmetric, if a o (b o c) - (a o b) o c = a o (c o b) - (a o c) o b, for any a, b, c epsilon A. The multiplication of right-symmetric Witt algebras W-n = {ud(i) : u epsilon U,U = K[x+1/1 , . . . , x+1/n], or = K[x(1), . . . , x(n)], i = 1, . . . , n}, p = 0, or W-n (m) = {ud(i) : u epsilon U,U = O-n(m)}, p > 0, are given by ud(i) o vd(j) = vd(j)(u)d(i). An analogue of the Amitsur-Levitzki theorem for right-symmetric Witt algebras is established. Right-symmetric Witt algebras of rank n satisfy the standard right-symmetric identity of degree 2 + 1 : Sigma(sigma epsilon Sym2n) sign(sigma)a(sigma(1)) o (a(sigma(2)) o . . . o (a(sigma(2n)) o a(2n+1)) . . . ) = 0. The minimal degree for left polynomial identities of W-n(r sym), W-n(+r sym), p = 0, is 2n + 1. All left polynomial identities of right-symmetric Witt algebras of minimal degree follow from the left standard right-symmetric identify s(2n)(r sym) = 0, if p not equal 2. (C) 2000 Academic Press.