Braiding and exponentiating noncommutative vector fields

Details Braiding and exponentiating noncommutative vector fields Braiding and exponentiating noncommutative vector fields

2003-06-05

arxiv.org/abs/math/0306094v1

Mathematics

Quantum Algebra

approx 27 pages, LATeX

Scientific paper

The purpose of this paper is to put into a noncommutative context basic notions related to vector fields from classical differential geometry. The manner of exposition is an attempt to make the material as accessible as possible to classical geometers. The definition of vector field used is a specialisation of the Cartan pair definition, and the paper relies on the idea of generalised braidings of 1-forms. The paper considers Kroneker deltas, interior products, Lie derivatives, Lie brackets, exponentiation of vector fields and parallel transport.

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