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We classify all groups and all pairs of absolutely simple Yetter–Drinfeld modules over such that the support of generates , , and the Nichols algebra of the direct sum of and 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.
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István Heckenberger, Leandro Vendramin, The classification of Nichols algebras over groups with finite root system of rank two. J. Eur. Math. Soc. 19 (2017), no. 7, pp. 1977–2017DOI 10.4171/JEMS/711