Title

Some Non-Koszul Algebras From Rational Homotopy Theory

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.

Volume

47

Issue

3

First Page

473

Last Page

482

Scholarly

yes

DOI

10.1112/blms/bdv019

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.

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