Homology, Homotopy and Applications

Volume 16 (2014)

Number 1

Cohomology of algebras over weak Hopf algebras

Pages: 341 – 369

DOI: https://dx.doi.org/10.4310/HHA.2014.v16.n1.a19

Authors

J. N. Alonso Álvarez (Departamento de Matemáticas, Universidade de Vigo, Spain)

J. M. Fernández Vilaboa (Departamento de Álxebra, Universidade de Santiago de Compostela, Spain)

R. González Rodríguez (Departamento de Matemática Aplicada II, Universidade de Vigo, Spain)

Abstract

In this paper we present the Sweedler cohomology for a cocommutative weak Hopf algebra $H$. We show that the second cohomology group classifies completely weak crossed products, having a common preunit, of $H$ with a commutative left $H$-module algebra A.

Keywords

weak Hopf algebra, Sweedler cohomology, weak crossed product

2010 Mathematics Subject Classification

16S40, 16T05, 18D10, 57T05

Published 2 June 2014