Some Non-Koszul Algebras From Rational Homotopy Theory
School of Science
Bulletin of the London Mathematical Society
The McCool group, denoted PΣnPΣn, is the group of pure symmetric automorphisms of a free group of rank nn. A presentation of the cohomology algebra H∗(PΣn,Q)H*(PΣn,Q) was determined by Jensen, McCammond, and Meier. We prove that H∗(PΣn,Q)H*(PΣn,Q) is a non-Koszul algebra for n⩾4n⩾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 PΣnPΣn, and prove that it has two natural decompositions as a smash product of algebras.
SMC Affiliated Work
Andrew Conner (Mathematics and Computer Science): “Some non-Koszul algebras from rational homotopy theory,” by A. Conner and P. Goetz, in the Bulletin of the London Mathematical Society (2015) 47 (3): 473-482; doi: 10.1112/blms/bdv019.
Conner, Andrew and Goetz, P.. Some Non-Koszul Algebras From Rational Homotopy Theory (2015). Bulletin of the London Mathematical Society. 47 (3), 473-482. 10.1112/blms/bdv019 [article]. https://digitalcommons.stmarys-ca.edu/school-science-faculty-works/39