Vol. 13, No. 5, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 6, 1343–1592
Issue 5, 1077–1342
Issue 4, 821–1076
Issue 3, 569–820
Issue 2, 309–567
Issue 1, 1–308

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
A five-term exact sequence for Kac cohomology

César Galindo and Yiby Morales

Vol. 13 (2019), No. 5, 1121–1144

We use relative group cohomologies to compute the Kac cohomology of matched pairs of finite groups. This cohomology naturally appears in the theory of abelian extensions of finite dimensional Hopf algebras. We prove that Kac cohomology can be computed using relative cohomology and relatively projective resolutions. This allows us to use other resolutions, besides the bar resolution, for computations. We compute, in terms of relative cohomology, the first two pages of a spectral sequence which converges to the Kac cohomology and its associated five-term exact sequence. Through several examples, we show the usefulness of the five-term exact sequence in computing groups of abelian extensions.

Hopf algebras, relative cohomology, abelian extensions of Hopf algebras
Mathematical Subject Classification 2010
Primary: 16T05
Received: 15 June 2018
Revised: 18 September 2018
Accepted: 22 February 2019
Published: 12 July 2019
César Galindo
Departamento de Matemáticas
Universidad de Los Andes
Yiby Morales
Departamento de Matemáticas
Universidad de los Andes