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
2014
Publication / Conference / Sponsorship
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
Rights
Open Access. Author manuscript (arXiv)
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.
Repository Citation
Conner, Andrew and Goetz, Pete. Some Non-Koszul Algebras From Rational Homotopy Theory (2014). 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
