Differential Calculus in Braided Abelian Categories

Details Differential Calculus in Braided Abelian Categories Differential Calculus in Braided Abelian Categories

1997-03-20

arxiv.org/abs/q-alg/9703036v2

Mathematics

Quantum Algebra

LaTeX2e, 39 pages, 2 style files attached (tar-file). Additional proofs in Chap. 1 for reader's convenience

Scientific paper

Braided non-commutative differential geometry is studied. In particular we investigate the theory of (bicovariant) differential calculi in braided abelian categories. Previous results on crossed modules and Hopf bimodules in braided categories are used to construct higher order bicovariant differential calculi over braided Hopf algebras out of first order ones. These graded objects are shown to be braided differential Hopf algebras with universal bialgebra properties. The article especially extends Woronowicz's results on (bicovariant) differential calculi to the braided non-commutative case.

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