Differential Calculus in Braided Abelian Categories
q-alg
2008-02-03 v2 Quantum Algebra
Abstract
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.
Cite
@article{arxiv.q-alg/9703036,
title = {Differential Calculus in Braided Abelian Categories},
author = {Yuri Bespalov and Bernhard Drabant},
journal= {arXiv preprint arXiv:q-alg/9703036},
year = {2008}
}
Comments
LaTeX2e, 39 pages, 2 style files attached (tar-file). Additional proofs in Chap. 1 for reader's convenience