Von Neumann algebras generated by two unitary operators u and v with u2Â =Â v3Â =Â 1

In this note, we prove that many von Neumann algebras can be generated by two unitary operators u and v with u2=v3=1. As applications, three important classes of II1 factors possessing this property are those with Property Γ, or with a Cartan masa, or non-prime ones.