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- W4300140804 abstract "Whereas the classical sphere $C P^1$ can be defined as the coordinate algebra generated by the matrix entries of a projector $e$ with $trace(e)=1$, the fuzzy-sphere is defined in the same way by $trace(e)=1+lambda$. We show that the standard $q$-sphere is similarly defined by $trace_q(e)=1$ and the Podles 2-spheres by $trace_q(e)=1+lambda$, thereby giving a unified point of view in which the 2-parameter Podles spheres are $q$-fuzzy spheres. We show further that they arise geometrically as `constant time slices' of the unit hyperboloid in $q$-Minkowski space viewed as the braided group $B_q[SU_2]$. Their localisations are then isomorphic to quotients of $U_q(su_2)$ at fixed values of the $q$-Casimir precisely $q$-deforming the fuzzy case. We use transmutation and twisting theory to introduce a $C_q[G_C]$-covariant calculus on general $B_q[G]$ and $U_q(g)$, and use $Omega(B_q[SU_2])$ to provide a unified point of view on the 3D calculi on fuzzy and Podles spheres. To complete the picture we show how the covariant calculus on the 3D bicrossproduct spacetime arises from $Omega(C_q[SU_2])$ prior to twisting." @default.
- W4300140804 created "2022-10-03" @default.
- W4300140804 creator A5074290225 @default.
- W4300140804 date "2008-12-29" @default.
- W4300140804 modified "2023-09-28" @default.
- W4300140804 title "q-Fuzzy spheres and quantum differentials on B_q[SU_2] and U_q(su_2)" @default.
- W4300140804 doi "https://doi.org/10.48550/arxiv.0812.4942" @default.
- W4300140804 hasPublicationYear "2008" @default.
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