Alladi Ramakrishnan Hall

On Hopf-Galois structures

Namrata Aravind

IMSc

Let K/F be a finite Galois extension of fields with Gal(K/F)=G. The Hopf algebra F[G] over F is an example of a Hopf-Galois structure on the extension $K/F$. The theory of Hopf-Galois structures for separable field extensions has been studied by number theorists under the field of Galois Module theory. This is closely related to the theory of skew braces which are known to give non-degenerate set theoretic solutions of the Yang-Baxter equation. In this talk I will give a brief history of the theory of Hopf-Galois structures and talk about the recent developments in classifying these structures. I will also talk about the work with my collaborator Dr. Saikat Panja on enumerating Hopf-Galois structures on groups of the form Zn ⋊ Z2.