$A^{G,\mu}$, which was studied in the Chapter \[chap: sklyanin\]. The algebra $B^{G,\mu}$ is shown — under some conditions — to have trivial centre in Proposition \[prop: centrethcrtwist\]. From this proposition we derive Corollary \[cor: centretwistskly\], which describes the centre of $A^{G,\mu}$. In §\[subsubsec: geomdescrthcrtwist\] we describe $B^{G,\mu}$ in terms of the geometric classification in [@artin2000semiprime], concerning semiprime, noetherian rings of quadratic growth. This description is given in Theorem \[thm: geomdescthcrtwist\], after which we show that the twist is a prime ring (Corollary \[cor: actuallyprime\]). The fat point modules over $A^{G,\mu}$ and the fact that $B^{G,\mu}$ possesses no point modules can both be related to this geometric realisation (see Propositions \[prop: onlyfatpoints\] and \[prop: fatpointsincohE\]).

Chapter \[chap: othertwists\] considers cocycle twists of other algebras, beginning in §\[subsec: staffordalgs\] with cocycle twists of algebras discovered by Stafford in [@stafford1994regularity]. The next examples are the algebras classified in [@rogalski2012regular] by Rogalski and Zhang. These are shown in Theorem \[thm: rogzhangmymain\] to have some hidden relations via cocycle twists. Of particular note amongst the remaining examples in the chapter is a twist of an algebra from [@vancliff1994quadratic] in §\[sec: vancliffql\]. We contrast the geometry relating to a factor ring of such a twist and 