報告題目：Hopf trusses an related structures in a monoidal setting
報 告 人：Ramón González Rodríguez
所在單位：University of Vigo
報告時間：2024年5月9日 20:00-22:00
報告地點：Zoom Id: 904 645 6677，Password: 2024
會議鍊接：
https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456
報告摘要: The main topic of this talk are certain algebraic structures that in recent years have received attention from numerous mathematicians. More concretely, in this talk we will present, in a braided monoidal setting, the main properties and categorical relationships between the categories of Hopf trusses, weak twisted post-Hopf algebras and weak twisted relative Rota-Baxter operators. The latter objects are a generalisation of the relative Rota-Baxter operators where the Rota-Baxter condition is modified through a cocycle. Also we will present the notion of generalized invertible 1-cocycle and we prove that the category of Hopf trusses is equivalent to the category of generalized invertible 1-cocycles. On the other hand, we also introduce the notions of module for a Hopf truss and for a generalized invertible 1-cocycle. We prove some functorial results involving these categories of modules and we show that the category of modules associated to a generalized invertible 1-cocycle is equivalent to a category of modules associated to a suitable Hopf truss. Finally, assuming the existence of equalizers, we introduce the notion of Hopf-module in the Hopf truss setting and we obtain the Fundamental Theorem of Hopf modules associated to a Hopf truss.
報告人簡介：Ramón González Rodríguez is a full professor at the Departament of Applied Mathematics II in the University of Vigo. His research interests is centered on Hopf algebras and and their generalizations as, for example, weak Hopf algebras, Hopf quasigroupos, groupoids, quasigroupoids, Hopf braces and Hopf trusses. His home page is https://dma.uvigo.es/~rgon/
