Uniqueness of addition in Lie algebras

Abstract: We say that a Lie ring R is called a unique addition Lie ring, or briefly a UA-Lie ring, if any commutator-preserving bijection on R preserves the addition as well. We prove that any semisimple Lie algebra and any its parabolic subalgebra is a UA-Lie ring. Also we describe wide classes of solvable UA-Lie rings.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar