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Cohomological dimensions of universal cosovereign Hopf algebras

Julien Bichon

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We compute the Hochschild and Gerstenhaber–Schack cohomological dimensions of the universal cosovereign Hopf algebras, when the matrix of parameters is a generic asymmetry. Our main tools are considerations on the cohomologies of free product of Hopf algebras, and on the invariance of the cohomological dimensions under graded twisting by a finite abelian group.

Article information

Publ. Mat., Volume 62, Number 2 (2018), 301-330.

Received: 28 November 2016
Revised: 9 March 2017
First available in Project Euclid: 16 June 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16T05: Hopf algebras and their applications [See also 16S40, 57T05] 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 16E10: Homological dimension

Hopf algebra cohomological dimensions Yetter–Drinfeld module


Bichon, Julien. Cohomological dimensions of universal cosovereign Hopf algebras. Publ. Mat. 62 (2018), no. 2, 301--330. doi:10.5565/PUBLMAT6221801.

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