

Quantum Galilei group as quantum reference frame transformations
By Giulia Gubitosi


Extremal eigenvectors, the spectral action, and the zeta spectral triple
By Alain Connes
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.