Minimal identities for right-symmetric algebras

An algebra A with multiplication A × A → A, (a, b) → a b, is called right-symmetric, if a (b c) − (a b) c = a (c b) − (a c ) b, for any a, b, c ε A. The multiplication of right-symmetric Witt algebras Wn = {d∂i : u ε U, U = K[x1±1, …, x±1n], or = K[x1, …, xn], i = 1, …, n},p = 0, or W(m) = {u∂i :u ε U, U = On.(m)}, p > 0, are given by u∂i u∂j = ν∂j(u)∂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 2n + 1 : ΣσεSym2n sign(σ)aσ(1) (aσ(2) … (aσ(2n) a2n+1) …) = 0. The minimal degree for left polynomial identities of Wnr sym, Wn+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 identity S2nr sym = 0, if p ≠ 2