Abstract
We explore finitely generated groups by studying the nilpotent towers and the various Lie algebras attached to such groups. Our main goal is to relate an isomorphism extension problem in the Postnikov tower to the existence of certain commuting diagrams. This recasts a result of Grigory Rybnikov in a more general framework and leads to an application to hyperplane arrangements, whereby we show that all the nilpotent quotients of a decomposable arrangement group are combinatorially determined.
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To the memory of Ştefan Papadima, 1953–2018
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A.I. Suciu partially supported by the Simons Foundation Collaboration Grant for Mathematicians # 354156.
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Porter, R.D., Suciu, A.I. Homology, lower central series, and hyperplane arrangements. European Journal of Mathematics 6, 1039–1072 (2020). https://doi.org/10.1007/s40879-019-00392-x
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DOI: https://doi.org/10.1007/s40879-019-00392-x
Keywords
- Lower central series
- Tower of nilpotent quotients
- Cohomology ring
- Associated graded Lie algebra
- Holonomy Lie algebra
- Malcev Lie algebra
- Hyperplane arrangement
- Decomposable arrangement