Quantum geometry of algebra factorisations and coalgebra bundles

Details Quantum geometry of algebra factorisations and coalgebra bundles Quantum geometry of algebra factorisations and coalgebra bundles

1998-08-15

arxiv.org/abs/math/9808067v2

Mathematics

Quantum Algebra

39 pages, LaTeX. Final version, to appear in Commun. Math. Phys

Scientific paper

We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras. An example is the factorisation of matrices $M_2(\C)=\C\Z_2\cdot\C\Z_2$. We also further extend the coalgebra version of theory introduced previously, to include frame resolutions and corresponding covariant derivatives and torsions. As an example, we construct $q$-monopoles on all the Podle\'s quantum spheres $S^2_{q,s}$.

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