2022/02/07 by Majid, Shahn, Simão, Francisco · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2202.03067
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 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(\Bbb C), the bicrossproduct model quantum spacetime in two dimensions and \Bbb Cq[SL2] for q a 4th root of unity.