Friday, 10 June 2011

qa.quantum algebra - Is there a good differential calculus for quantum SU(3)?

For quantum $SU(2)$, Woronowicz gave a well differential calculus. If we denote the generators of quantum $SU(2)$ by $a,b,c,d$, then the ideal of ker($epsilon)$ corresponding to this calculus is
$$
< a+ q^2d - (1+q^2),b^2,c^2,bc,(a-1)b,(d-1)c>.
$$
This calculus can be shown to generalise the classical calculus on $SU(2)$ when $q=1$. Does anyone know of a (good) calculus (and its ideal) for quantum $SU(3)$?

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