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arXiv · 1407.4726

Some non-Koszul algebras from rational homotopy theory

Andrew Conner·Peter Goetz
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Abstract

The McCool group, denoted $P\Sigma_n$, is the group of pure symmetric automorphisms of a free group of rank $n$. The cohomology algebra $H^*(P\Sigma_n, \mathbb{Q})$ was determined by Jensen, McCammond and Meier. We prove that $H^*(P\Sigma_n, \mathbb{Q})$ is a non-Koszul algebra for $n \geq 4$, 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 $P\Sigma_n$, and prove that it has two natural decompositions as a smash product of algebras.

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Andrew Conner, Peter Goetz. 2014-07-17. Some non-Koszul algebras from rational homotopy theory. https://doi.org/10.1112/blms/bdv019

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