# Noncommutative differentials on quantum groups and pre-Lie algebra

**Datum:**24 maart 2017

**Locatie:**G.005 - Middelheimlaan 1 - 2020 Antwerpen (route: UAntwerpen, Campus Middelheim)

**Tijdstip:**14 uur

**Korte beschrijving:**Seminar by Wenqing Tao

**Abstract**

Noncommutative differentials theory in new directions of generalised differentials, codifferentials and pre-Lie algebras is studied. We obtain duality results like left covariant differentials on U(g) are classified by Lie algebra 1-cocycles while group 1-cocycles correspond to codifferential structures on algebraic groups. One of many interesting construction we find is that first order calculus on a Hopf algebra can extend canonically to all orders via the braided super-shuffle algebra.

If time permits, I will show that the quantisation of a connected simply-connected Poisson-Lie group admits a left-covariant noncommutative differential structure at lowest deformation order if and only if the dual of its Lie algebra admits a pre-Lie algebra structure. This talk is based on the joint work with Shahn Majid.

**Link:**https://www.uantwerpen.be/en/rg/fundamental-mathematics/