Classification of Differentials on Quantum Doubles and Finite Noncommutative Geometry
نویسنده
چکیده
We discuss the construction of finite noncommutative geometries on Hopf algebras and finite groups in the ‘quantum groups approach’. We apply the author’s previous classification theorem, implying that calculi in the factorisable case correspond to blocks in the dual, to classify differential calculi on the quantum codouble C(G)◮<CG = D∗(G) of a finite group G. We give D∗(S3) as an example. We explain the geometric meaning of the Woronowicz construction for higher forms in terms of a Hodge * operator.
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