Homology, Homotopy and Applications

Cohomology of algebras over weak Hopf algebras

J. N. Alonso Álvarez, J. M. Fernández Vilaboa, and R. González Rodríguez

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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 $A$.

Article information

Source
Homology Homotopy Appl., Volume 16, Number 1 (2014), 341-369.

Dates
First available in Project Euclid: 3 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.hha/1401800087

Mathematical Reviews number (MathSciNet)
MR3217310

Zentralblatt MATH identifier
1296.57025

Subjects
Primary: 57T05: Hopf algebras [See also 16T05] 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23] 16T05: Hopf algebras and their applications [See also 16S40, 57T05] 16S40: Smash products of general Hopf actions [See also 16T05]

Keywords
Weak Hopf algebra Sweedler cohomology weak crossed product

Citation

Álvarez, J. N. Alonso; Vilaboa, J. M. Fernández; Rodríguez, R. González. Cohomology of algebras over weak Hopf algebras. Homology Homotopy Appl. 16 (2014), no. 1, 341--369. https://projecteuclid.org/euclid.hha/1401800087


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