slideshow 3

Noncommutative Geometry and Topology in Prague

Quantum Jet Bundles

Speaker’s name: 
Francisco Manuel Castela Simão
Speaker’s affiliation: 
Queen Mary University of London

 

Place: 
This talk will take place in the blue seminar room, back building, Žitná 25.

It will also be broadcast on Zoom:
https://cesnet.zoom.us/j/91975183920?pwd=SGdlRUhLS21HUnVFTXBKcE1vYXlrQT09
Meeting ID: 919 7518 3920
Passcode: 102707
Date: 
Tuesday, 15. November 2022 - 16:00 to 17:00
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’ \sigma\colon \Omega^1 \otimes_A \Omega^1_A \to \Omega^1 \otimes_A \Omega^1_A  obey the Yang-Baxter equation or braid relations. We then build the jet bundle on the graded vector space of symmetric tensors as a braided Hopf algebra \Omega_S with of respect to \sigma. 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 \sigma_E obeying the coloured braid relations. Examples include the permutation group S_3 with its 2-cycles calculus and the 2×2 matrices M_2(\mathbb(C)).