Homology, Homotopy and Applications

Volume 22 (2020)

Number 2

An elementary computation of the cohomology of the Fomin–Kirillov algebra with $3$ generators

Pages: 367 – 386

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n2.a22


Estanislao Herscovich (Institut Fourier, Université Grenoble Alpes, Gières, France)


We give an elementary computation of the algebra structure of the Yoneda algebra of the Fomin–Kirillov algebra FK(3) over a field of characteristic different from $2$ and $3$. The computation is based on a new bootstrap technique we introduce which is built upon the (nonacyclic) Koszul complex of FK(3).


Koszul algebras, Yoneda algebra, Fomin–Kirillov algebras, Nichols algebras

2010 Mathematics Subject Classification

16S37, 16T05, 18G15

Received 23 September 2019

Received revised 20 February 2020

Accepted 21 February 2020

Published 20 May 2020