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arXiv · 2202.03067

Quantum Jet Bundles

Shahn Majid·Francisco Simão
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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' $σ:Ω^1\otimes_AΩ^1\to Ω^1\otimes_AΩ^1$ 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 $σ_E$ obeying the coloured braid relations. Examples include the permutation group $S_3$ with its 2-cycles calculus, $M_2(\Bbb C)$, the bicrossproduct model quantum spacetime in two dimensions and $\Bbb C_q[SL_2]$ for $q$ a 4th root of unity.

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BibTeXRIS

Shahn Majid, Francisco Simão. 2023-05-16. Quantum Jet Bundles. https://arxiv.org/abs/2202.03067

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