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Finite-Dimensional Pointed Hopf Algebras Over Finite Simple Groups of Lie Type IV. Unipotent Classes in Chevalley and Steinberg Groups

  • Nicolás Andruskiewitsch
  • Giovanna Carnovale
  • Gastón Andrés GarcíaEmail author
Article

Abstract

We show that all unipotent classes in finite simple Chevalley or Steinberg groups, different from PSLn(q) and PSp2n(q), collapse (i.e. are never the support of a finite-dimensional Nichols algebra), with a possible exception on one class of involutions in PSUn(2m).

Keywords

Nichols algebra Hopf algebra Rack Finite group of Lie type Conjugacy class 

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Notes

Acknowledgments

At different stages of this project, Mauro Costantini, Paolo Papi and Jay Taylor, helped us with interesting conversations and precise references. We thank them a lot. We thank also the referee for his/her suggestions.

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Authors and Affiliations

  1. 1.FaMAFUniversidad Nacional de Córdoba, CIEM – CONICETCórdobaArgentina
  2. 2.Dipartimento di Matematica Tullio Levi-CivitaUniversità degli Studi di PadovaPadovaItaly
  3. 3.Departamento de Matemática, Facultad de Ciencias ExactasUniversidad Nacional de La Plata, CONICETLa PlataArgentina

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