We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from () collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra whose group of group-like elements is 2(), ΩΩ+4(), ΩΩ−4(), 34(), 7(), 8(), 4(), or 2() with q even is the group algebra.
Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V. Mixed classes in Chevalley and Steinberg groups
Giovanna Carnovale
;
2021
Abstract
We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from () collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra whose group of group-like elements is 2(), ΩΩ+4(), ΩΩ−4(), 34(), 7(), 8(), 4(), or 2() with q even is the group algebra.
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Andruskiewitsch2021_Article_Finite-dimensionalPointedHopfA.pdf
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