Quantum Jet Bundles
Abstract
We formulate a notion of jet bundles over a possibly noncommutative algebra A equipped with a torsion free connection. Among the conditions needed for 3rd-order jets and above is that the connection also be flat and its `generalised braiding tensor' σ:1A1 1A1 obey the Yang-Baxter equation or braid relations. We also cover the case of jet bundles of a given `vector bundle' over A in the form of a bimodule E with a flat bimodule connection with its braiding σE obeying the coloured braid relations. Examples include the permutation group S3 with its 2-cycles calculus, M2( C), the bicrossproduct model quantum spacetime in two dimensions and Cq[SL2] for q a 4th root of unity.
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