“…The Fomin-Kirillov algebra E n [7] is a certain noncommutative algebra with generators x ij for 1 ≤ i < j ≤ n that satisfy a simple set of quadratic relations. While it was originally introduced as a tool to study the structure constants for Schubert polynomials, since then the Fomin-Kirillov algebra and its generalizations have received much attention from the perspectives of both combinatorics and algebra: see, for instance, [3,8,13,14,15,16,18,20,21,23,26]. But despite its simple presentation, even some basic questions about E n have eluded an answer thus far, such as whether or not it is finite-dimensional for n ≥ 6.…”