Twisting of homogeneous algebras

Twisting process for homogeneous algebras is defined. It consists of a particular kind of actual deformations controlled by a multiplicative cosimplicialquasicomplex related to each homogeneous algebra. The elements implementing twist transformations are a subclass of the counital 2-cocycles of . Such transformations are studied by means of their co-homological properties. It is shown they define an equivalence relation between homogeneous algebras, in such a way that cubic Artin–Schelter regular algebras of type S1 (including parafermionic and plactic algebras with two generators) belong to the same class.