Algebraic and measurable embeddings between square-free right-angled Artin groups

Adrien Abgrall, Alexandra Gurieva, Camille Horbez

Let $\Gamma ,\Delta$ be finite simplicial graphs, and assume that $\Gamma$ has no induced squares. We prove that the right-angled Artin group $A(\Delta )$ measurably embeds into $A(\Gamma )$ if and only if $A…