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PreprintarXiv licencearXiv

Higher Fomin-Kirillov algebras are infinite-dimensional

  • N. Andruskiewitsch
  • I. Angiono
  • I. Heckenberger
  • S. Lentner
  • C. Reiher
  • L. Vendramin
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Abstract

We show that the Fomin--Kirillov algebras FKn are infinite-dimensional for n≥6. This answers a question posed by Fomin and Kirillov in 1997. To prove this, we demonstrate that the Nichols algebras supported on the conjugacy class of transpositions of the symmetric group are infinite-dimensional for both relevant 2-cocycles. For this, we develop a new method of partially semisimplifying a Nichols algebra along an automorphism of order p in characteristic p.

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Cite

BibTeXRIS
BibTeX
@misc{andruskiewitsch2026higher,
  title = {{Higher Fomin-Kirillov algebras are infinite-dimensional}},
  author = {N. Andruskiewitsch and I. Angiono and I. Heckenberger and S. Lentner and C. Reiher and L. Vendramin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10144},
  eprint = {2610.10144},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10144},
}
RIS
TY  - UNPB
TI  - Higher Fomin-Kirillov algebras are infinite-dimensional
AU  - N. Andruskiewitsch
AU  - I. Angiono
AU  - I. Heckenberger
AU  - S. Lentner
AU  - C. Reiher
AU  - L. Vendramin
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.10144
UR  - https://arxiv.org/abs/2610.10144
AB  - We show that the Fomin--Kirillov algebras FK_n are infinite-dimensional for n≥6. This answers a question posed by Fomin and Kirillov in 1997. To prove this, we demonstrate that the Nichols algebras supported on the conjugacy class of transpositions of the symmetric group are infinite-dimensional for both relevant 2-cocycles. For this, we develop a new method of partially semisimplifying a Nichols algebra along an automorphism of order p in characteristic p.
ER  -