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

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).

Keywords

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

2010 Mathematics Subject Classification

16S37, 16T05, 18G15

Full Text (PDF format)

Received 23 September 2019

Received revised 20 February 2020

Accepted 21 February 2020

Published 20 May 2020