Title：Regular subgroups, skew braces, gamma functions and Rota–Baxter operators

Reporter：Andrea Caranti

Work：University of Trento, Italy

Time：2023年4月19日 20:00-22:00

Address：ZOOM Id：904 645 6677，Password：2023

Link：https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09

Summary of report: Skew braces, a novel algebraic structure introduced only in 2015, have already spawned a sizeable literature. The skew braces with a given additive group structure correspond to the regular subgroups of the permutational holomorph of such a group. These regular subgroups can in turn be described in terms of certain so-called gamma functions from the group to its automorphism group, which are characterised by a functional equation. We will show how gamma functions can be used in studying skew braces, underlining in particular their relationship to Rota-Baxter operators.

Brief introduction of reporter：Andrea Caranti is a Senior Professor of Algebra at the University of Trento, Italy. He has worked mainly in group theory (nilpotent groups, automorphisms, applications to cryptography) and on graded, modular Lie algebras. His recent work concerns group-theoretical aspects of skew braces.