Bi-quadratic algebras on 3 generators with PBW: class II.1

In \cite{BigAlg-3gen}, an explicit description of bi-quadratic algebras on three generators with PBW basis was obtained. There are four classes: I-IV. The aim of the paper is to study algebras that belong to one of the classes: class II.1. In this class, there are twelve distinct subclasses to consider. The aim of the paper is to study these algebras. In particular, the centre, the primes ideals, the automorphism groups and the normal elements are explicitly described. The Krull, classical Krull, global and Gelfand-Kirillov dimensions of the algebras and their tensor products are computed.