Infinite dimensional, affine nil algebras A⊗AopA⊗Aop and A⊗AA⊗A exist

In this paper we answer two questions posed by Puczyłowski in 1993, by constructing, over any algebraically closed field K, a finitely generated, infinite dimensional algebra A   such that the algebras A⊗KAA⊗KA and A⊗KAopA⊗KAop are nil.