Some non‐Koszul algebras from rational homotopy theory. (23rd March 2015) - Conner, A.; Goetz, P.
Abstract : The McCool group, denotedP Σ n, is the group of pure symmetric automorphisms of a free group of rankn . A presentation of the cohomology algebraH * ( P Σ n, Q ) was determined by Jensen, McCammond, and Meier. We prove thatH * ( P Σ n, Q ) is a non‐Koszul algebra forn ⩾ 4, which answers a question of Cohen and Pruidze. We also study the enveloping algebra of the graded Lie algebra associated to the lower central series ofP Σ n, and prove that it has two natural decompositions as a smash product of algebras.