XL Workshop on Geometric Methods in Physics Białowieża, 2-8.07.2023 XII School on Geometry and Physics Białystok, 26-30.06.2023

Anastasia Doikou

Quantum groups, discrete Magnus expansion, pre-Lie & tridendriform algebras

We review the discrete evolution problem and the corresponding solution as a discrete Dyson series in order to rigorously derive a discrete version of Magnus expansion. We also systematically derive the discrete analogue of the pre-Lie Magnus expansion and show that the elements of the discrete Dyson series are expressed in terms of a tridendriform algebra action. Key links between quantum algebras, tridendriform and pre-Lie algebras are then established. This is achieved by examining tensor realizations of quantum groups, such as the Yangian. We show that these realizations can be expressed in terms of tridendriform and pre-Lie algebras actions.
Event sponsored by
University of Białystok
University of Białystok
Doskonala Nauka