Calculi, cohomology, and Hopf algebroids

Niels Kowalzig (U Napoli)

Sep 13. 2021, 14:00 — 15:00

We will discuss in which sense bialgebroids and (left) Hopf algebroids can be seen as a notion that unifies various (co)homology theories such as Hochschild, Lie algebroid (in particular Lie algebra and Poisson), or group and etale groupoid (co)homology. We then pass to so-called higher structures on these (co)homoogy groups like cup and cap products, Gerstenhaber algebras or those of Batalin-Vilkovisky modules, i.e., of a noncommutative differential calculus that, among other things, comes along with a contraction, a Lie derivative and a differential. As an illustration, we show how the well-known corresponding operators from differential geometry in the classical Cartan homotopy formula can be obtained from this general approach.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Geometry for Higher Spin Gravity: Conformal Structures, PDEs, and Q-manifolds (Thematic Programme)
Xavier Bekaert (U Tours)
Andreas Cap (U of Vienna)
Stefan Fredenhagen (U of Vienna)
Maxim Grigoriev (Lebedev Inst. & Lomonosov Moscow SU)
Alexei Kotov (U Hradec Králové)