A nonzero element of degree 7 in the center of the free alternative algebra

摘要

We present a nonzero element of degree 7 in the center of the free alternative algebra over a field of characteristic 0 or greater than 7. This element is u = Sigma(piis an element ofS7)sgn(pi)((a(pi(1)), a(pi(2)), a(pi(3))), a(pi(4)), (a(pi(5)); a(pi(6)), a(pi(7)))). This element is Malcev admissible and for the corresponding element w in a free Malcev algebra M of characteristic 0 or greater than 7, one gets that wM = 0. [References: 12]