On two letter identities in Lie rings

Boris Baranov, Sergei O. Ivanov, Savelii Novikov

Let $L=L(a,b)$ be a free Lie ring on two letters $a,b.$ We investigate the kernel $I$ of the map $L\oplus L\to L$ given by $(A,B)\mapsto [A,a]+[B,b].$ Any homogeneous element of…