Geodesic
The classification of Nichols algebras over groups with finite root system of rank two
Journal of the European Mathematical Society, Tome 19 (2017) no. 7, pp. 1977-2017 Cet article a éte moissonné depuis la source EMS Press

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We classify all groups G and all pairs (V,W) of absolutely simple Yetter–Drinfeld modules over G such that the support of V⊕W generates G, cW,V​cV,W​=id, and the Nichols algebra of the direct sum of V and W admits a finite root system. As a byproduct, we determine the dimensions of such Nichols algebras, and several new families of finite-dimensional Nichols algebras are obtained. Our main tool is the Weyl groupoid of pairs of absolutely simple Yetter–Drinfeld modules over groups.
DOI : 10.4171/jems/711
Classification : 16-XX, 20-XX
Keywords: Hopf algebra, Nichols algebra, Weyl groupoid 
@article{JEMS_2017_19_7_a2,
     author = {Istv\'an Heckenberger and Leandro Vendramin},
     title = {The classification of {Nichols} algebras over groups with finite root system of rank two},
     journal = {Journal of the European Mathematical Society},
     pages = {1977--2017},
     year = {2017},
     volume = {19},
     number = {7},
     doi = {10.4171/jems/711},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/711/}
}
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István Heckenberger; Leandro Vendramin. The classification of Nichols algebras over groups with finite root system of rank two. Journal of the European Mathematical Society, Tome 19 (2017) no. 7, pp. 1977-2017. doi: 10.4171/jems/711

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