Given $q \in C$ invertible, Kassel says that a $M_q(2)$ point of an $R$ algebra is a $m=\left(\begin{array}{cc} A & B\\ C & D \end{array}\right)\in R^{4}$ such that $A,\,B,\,C,\,D \in R$ satisfy the following relations $$CA=qAC,$$$$ DB=qBD, $$$$BA=qAB,$$$$DC=qCD,$$$$BC=CB$$$$DA-qCB=AD-\left(q^{-1}\right)BC.$$ Can anybody give me a concrete example of $M_3(C)$ matrices that form such a point? If it's not possible in $M_3(C)$, every othere concrete example is weel accepted. Thanks in advance

  • $\begingroup$ I guess you probably prefer non-zero $A,B,C,D$? $\endgroup$ – Casteels Jul 6 '18 at 16:55
  • $\begingroup$ Indeed I prefer non trivial examples $\endgroup$ – Dac0 Jul 7 '18 at 17:21

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