New interactions between categorical algebra and Hopf algebra theory
(2018) CatAlg2018 — Location: Gargnano, organized by the Università degli Studi di Milano (29.May.2018)
Files
AbstractGran.pdf
Open Access - Adobe PDF
- 115.02 KB
Details
- Authors
- Abstract
- Some properties of the category of cocommutative Hopf algebras have been recently explored from the perspective of categorical algebra. Most of the results in this direction have been obtained under the assumption that the characteristic of the base field K is zero. In the present work with F. Sterck and J. Vercruysse we drop this assumption, and establish some properties of the category HopfK,coc of cocommutative Hopf algebras over an arbitrary field K. In this talk we prove that the category HopfK,coc is semi-abelian and action representable. This result can be seen as a non-abelian version of Takeuchi’s classical theorem asserting that the category of commutative and cocommutative Hopf algebras is abelian. We shall then make a few remarks on the notion of center in HopfK,coc, and give an example of a localization in the semi-abelian category HopfK,coc. Some possible developments in categorical Galois theory will also be discussed.
- Affiliations
Citations
Gran, M. (2018). New interactions between categorical algebra and Hopf algebra theory. CatAlg2018, Gargnano, organized by the Università degli Studi di Milano. https://hdl.handle.net/2078.5/123554