Weakly confluent quadratic algebras (Q1281927)

A classical result by \textit{S. B. Priddy} [see Trans. Am. Math. Soc. 152, 39-60 (1970; Zbl 0261.18016)] states that a quadratic algebra which has a PBW-basis (in the terminology of the paper under review: is weakly confluent) must be a Koszul algebra. In a recent paper [see J. Algebra 201, No. 1, 243-283 (1998; Zbl 0915.16025)], \textit{R. Berger} has given a new proof of Priddy's theorem which is based on properties of a lattice of vector spaces defined by so-called reduction operators. The paper under review continues this line of thought. In particular, it is shown (by an explicit classification) that conversely Koszul implies weakly confluent if the algebra has just two generators. For algebras with three generators, a counterexample is provided.