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

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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).

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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. FaMAF, Universidad Nacional de Córdoba, CIEM – CONICET, Medina Allende s/n (5000) Ciudad Universitaria, Córdoba, Argentina

    Nicolás Andruskiewitsch

  2. Dipartimento di Matematica Tullio Levi-Civita, Università degli Studi di Padova, via Trieste 63, 35121, Padova, Italy

    Giovanna Carnovale

  3. Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CONICET, C. C. 172, 1900, La Plata, Argentina

    Gastón Andrés García

Authors
  1. Nicolás Andruskiewitsch
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  2. Giovanna Carnovale
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  3. Gastón Andrés García
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Corresponding author

Correspondence to Gastón Andrés García.

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Presented by: Peter Littelmann

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The work of N. A. was partially supported by CONICET, Secyt (UNC) and the MathAmSud project GR2HOPF. The work of G. C. was partially supported by Progetto di Ateneo dell’Università di Padova: CPDA125818/12. The work of G. A. G. was partially supported by CONICET, Secyt (UNLP) and ANPCyT-Foncyt 2014-0507. The results were obtained during visits of N. A. and G. A. G. to the University of Padova, and of G. C. to the University of Córdoba, partially supported by the bilateral agreement between these Universities, the Erasmus Mundus Action 2 Programme AMIDILA and the Visiting Scientist program of the University of Padova.

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Andruskiewitsch, N., Carnovale, G. & García, G.A. Finite-Dimensional Pointed Hopf Algebras Over Finite Simple Groups of Lie Type IV. Unipotent Classes in Chevalley and Steinberg Groups. Algebr Represent Theor 23, 621–655 (2020). https://doi.org/10.1007/s10468-019-09868-6

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