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arXiv · 2610.10144

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 $FK_n$ are infinite-dimensional for $n\geq6$. 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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N. Andruskiewitsch, I. Angiono, I. Heckenberger, S. Lentner, C. Reiher, L. Vendramin. 2026-10-07. Higher Fomin-Kirillov algebras are infinite-dimensional. https://arxiv.org/abs/2610.10144

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