Title: Hopf Trusses and Related Structures in a Monoidal Setting
Speaker: Ramón González Rodríguez
Institution: University of Vigo
Date & Time: May 9, 2024, 20:00–22:00
Location: Zoom ID: 904 645 6677, Password: 2024
This talk focuses on algebraic structures that have garnered attention from mathematicians in recent years. Specifically, we will present the main properties and categorical relationships between the categories of Hopf trusses, weak twisted post-Hopf algebras, and weak twisted relative Rota-Baxter operators within a braided monoidal framework. The latter generalize relative Rota-Baxter operators by modifying the Rota-Baxter condition via a cocycle. We will introduce the notion of generalized invertible 1-cocycles and prove that the category of Hopf trusses is equivalent to the category of such cocycles.
Additionally, we define modules for Hopf trusses and generalized invertible 1-cocycles, establishing functorial results and showing that the module category for a generalized invertible 1-cocycle is equivalent to that of a suitable Hopf truss. Assuming the existence of equalizers, we introduce Hopf modules in the Hopf truss setting and derive the Fundamental Theorem of Hopf Modules for this context.
Ramón González Rodríguez is a full professor in the Department of Applied Mathematics II at the University of Vigo. His research focuses on Hopf algebras and their generalizations, including weak Hopf algebras, Hopf quasigroups, groupoids, quasigroupoids, Hopf braces, and Hopf trusses. His academic homepage is https://dma.uvigo.es/~rgon/.
