Quantum geometry of algebra factorisations and coalgebra bundles

1998/08/15 by Tomasz Brzezinski, Shahn Majid, Brzezinski, Tomasz +1
Mathematics · Physics and Astronomy · #81R50 58B30 16W30 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #msc:16W30 #msc:58B30 #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/9808067

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

arxiv created 2000/05/18 · arxiv updated 2009/11/30

Abstract

We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras. An example is the factorisation of matrices M₂(\C)=\C\Z₂⋅\C\Z₂. 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 Podleś quantum spheres S²_q,s.

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