Annals of K-Theory 8-4 (2023), 669--692; doi:10.2140/akt.2023.8.669; arXiv:2201.07153

François Digne and Christian Kassel

Braid groups and symplectic Steinberg groups

Mathematics Subject Classification (2000): (Primary) 19C09, 20G30, 20F36; (Secondary) 11E57, 20F05, 22E40

Abstract. We construct a homomorphism f from the braid group B_2n+2 on 2n + 2 strands to the Steinberg group St(C_n,Z) associated with the Lie type C_n and with integer coefficients. This homomorphism lifts the well-known symplectic representation of the braid groups. We also describe the image and the kernel of f.

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(6 December 2023)