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:Ω1⊗AΩ1→Ω1⊗AΩ1 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 flat bimodule connection with its braiding σEobeying the coloured braid relations. Examples include the permutation group S3 with its 2-cycles calculus, M2(ℂ) and the bicrossproduct model quantum spacetime in two dimensions.

rings and algebrasrepresentation theory

Audience: researchers in the topic

ONCAS Online Noncommutative Algebra Seminar

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