Speaker:
Ralph Martin Kaufmann
Zugehörigkeit:
Purdue University, West Lafayette/MPIM
Datum:
Don, 25/07/2019 - 15:00 - 16:00
We will discuss how simplicial and categorical structures lead to Hopf algebras.
In particular, we will focus on Joyal duality to give a simple explanation of the co-product given by Goncharov
for multi-zeta values and its graphical depiction. In this setting, co-actions also appear naturally. We further show that
his type of Hopf algebracomes from a categorical setup, where the product is a monoidal product and the co-product is
dual to the partial productthat is given by composition of morphisms, providing a simple "raison d'être" for these
"prima vista" complicated co-products. In this setting, we see the analogous structure of the Hopf algebra of Goncharov
and those of Connes and Kreimer.