## Algebra and Combinatorics Seminar

**Date:** October 13, 2017

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 117

**Speaker:** Yiby Morales, Universidad de los Andes

**Title:** *The five-term exact sequence for Kac cohomology*

**Abstract:** The group of equivalence classes of abelian extensions of Hopf algebras associated to a matched pair of finite groups was described by Kac in the 60’s as the first cohomology group of a double complex, whose total cohomology is known as the Kac cohomology. Masuoka generalized this result and used it to compute some groups of abelian Hopf algebra extensions. Since Kac cohomology is defined as the total cohomology of a double complex, there is an associated spectral sequence. I will explain how we compute the five-term exact sequence associated to this double complex, which can be used to compute some other groups of abelian extensions. This is joint work with César Galindo.