Representing subalgebras as retracts of finite subdirect powers

Abstract

We prove that if $\mathbb A$ is an algebra that is supernilpotent with respect to the $2$-term higher commutator, and $\mathbb B$ is a subalgebra of $\mathbb A$, then $\mathbb B$ is representable as a retract of a finite subdirect power of $\mathbb A$.