Geodesic
On the computation of Hopf 2-cocycles with an example of diagonal type
Glasgow mathematical journal, Tome 65 (2023) no. 1, pp. 141-169

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DOI

We present a framework for the computation of the Hopf 2-cocycles involved in the deformations of Nichols algebras over semisimple Hopf algebras. We write down a recurrence formula and investigate the extent of the connection with invariant Hochschild cohomology in terms of exponentials. As an example, we present detailed computations leading to the explicit description of the Hopf 2-cocycles involved in the deformations of a Nichols algebra of Cartan type $A_2$ with $q=-1$, a.k.a. the positive part of the small quantum group $\mathfrak{u}^+_{\sqrt{-\text{1}}}(\mathfrak{sl}_3)$. We show that these cocycles are generically pure, that is they are not cohomologous to exponentials of Hochschild 2-cocycles.
DOI : 10.1017/S0017089522000192
Mots-clés : Hopf algebras, deformations, cohomology 
Iglesias, Agustín García; Sánchez, José Ignacio. On the computation of Hopf 2-cocycles with an example of diagonal type. Glasgow mathematical journal, Tome 65 (2023) no. 1, pp. 141-169. doi: 10.1017/S0017089522000192
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     title = {On the computation of {Hopf} 2-cocycles with an example of diagonal type},
     journal = {Glasgow mathematical journal},
     pages = {141--169},
     year = {2023},
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