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.
Julien Bichon. "Cohomological dimensions of universal cosovereign Hopf algebras." Publ. Mat. 62 (2) 301 - 330, 2018. https://doi.org/10.5565/PUBLMAT6221801