#### Title

Some Non-Koszul Algebras From Rational Homotopy Theory

#### SMC Affiliated Work

1

#### Status

Faculty

#### School

School of Science

#### Department

Math/Computer Science

#### Document Type

Article

#### Publication Date

2015

#### Publication Title

Bulletin of the London Mathematical Society

#### Description/Abstract

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.

#### Scholarly

yes

#### DOI

10.1112/blms/bdv019

#### Volume

47

#### Issue

3

#### First Page

473

#### Last Page

482

#### Disciplines

Mathematics

#### Original Citation

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.

#### Recommended Citation

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