Braided bimodules, quantum jet bundles and quantum geodesics

By Shahn Majid

Appears in collection : 2023 - T2 - WS1 - GAP XVIII: Homotopy algebras and higher structures

We show how solutions of the Yang-Baxter or braid relations on bimodules over a possibly noncommutative algebra arise naturally in the context of bimodule connections in noncommutative geometry. As an application, we show how such connections can be used to define a notion of quantum jet bundle in work with F. Simao. We also show in work with E. Beggs how the same idea applied to A-B bimodule connections lead to a notion of quantum geodesics on A with parameter space algebra B and are already present for A the Heisenberg algebra in quantum mechanics.

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  • DOI 10.57987/IHP.2023.T2.WS1.001
  • Cite this video Majid, Shahn (23/05/2023). Braided bimodules, quantum jet bundles and quantum geodesics. IHP. Audiovisual resource. DOI: 10.57987/IHP.2023.T2.WS1.001
  • URL https://dx.doi.org/10.57987/IHP.2023.T2.WS1.001

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