Abstrak

Kembali

The McCool group, denoted PΣn, is the group of pure symmetric automorphisms of a free group of rank n. A presentation of the cohomology algebra H∗(PΣn,Q) was determined by Jensen, McCammond, and Meier. We prove that H∗(PΣn,Q) is a non-Koszul algebra for n >= 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 of PΣn, and prove that it has two natural decompositions as a smash product of algebras.