A Fomin-Kirillov algebra 
over a field of field
characteristic zero is the associative algebra
generated by 
for 
with quadratic relations
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
where the middle two relations hold for 
and the last for pairwise distinct 
, 
, 
, and 
with 
and 
.
The algebras are finite-dimensional for 
, 4, and 5. Andruskiewitsch et al. (2026) proved that
is infinite-dimensional for every 
. Andruskiewitsch et al. (2026) credit GPT-6 Astra
with suggesting a proof strategy for the case 
, which they partly adopted and partly developed within a
more general argument.
