Finite generation of Lie algebras associated to associative algebras

Original · EN

Let F be a field of characteristic not 2. An associative F-algebra R gives rise to the commutator Lie algebra R⁽⁻⁾=(R,[a,b]=ab-ba). If the algebra R is equipped with an involution *:R→ R then the space of the skew-symmetric elements K={a ∈ R a*=-a } is a Lie subalgebra of R⁽⁻⁾. In this paper we find sufficient conditions for the Lie algebras [R,R] and [K,K] to be finitely generated.