Some aspects of braided geometry: differential calculus, tangent space, gauge theory

Details Some aspects of braided geometry: differential calculus, tangent space, gauge theory Some aspects of braided geometry: differential calculus, tangent space, gauge theory

1999-06-22

arxiv.org/abs/math/9906144v1

J.Phys.A32:4183-4197,1999

Mathematics

Quantum Algebra

19 pages, Latex

Scientific paper

10.1088/0305-4470/32/23/301

A new approach is suggested to quantum differential calculus on certain quantum varieties. It consists in replacing quantum de Rham complexes with differentials satisfying Leibniz rule by those which are in a sense close to Koszul complexes from \cite{G1}. We also introduce the tangent space on a quantum hyperboloid equipped with an action on the quantum function space and define the notions of quantum (pseudo)metric and quantum connection (partially defined) on it. All objects are considered from the viewpoint of flatness of quantum deformations. A problem of constructing a flatly deformed quantum gauge theory is discussed as well.

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