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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Volume 326, Pages 293–310
DOI: https://doi.org/10.4213/tm4425 (Mi tm4425) 		 
Polyhedral Products, Graph Products, and $p$-Central Series

Taras E. Panovabcd, Temurbek A. Rahmatullaevbd

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
c Institute for Theoretical and Experimental Physics of National Research Centre “Kurchatov Institute”, Moscow, Russia
d National Research University Higher School of Economics, Moscow, Russia
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DOI: https://doi.org/10.4213/tm4425
Abstract: We relate polyhedral products of topological spaces to graph products of groups. The loop homology algebras of polyhedral products are identified with the universal enveloping algebras of the Lie algebras associated with central series of graph products. As an application, we describe the restricted Lie algebra associated with the lower $2$-central series of a right-angled Coxeter group and identify its universal enveloping algebra with the loop homology of the Davis–Januszkiewicz space.
Keywords: polyhedral product, graph product, right-angled Coxeter group, central series, restricted Lie algebra, loop homology.
Funding agency Grant number
Russian Science Foundation 23-11-00143
HSE Basic Research Program
The work of Taras Panov (Sections 2, 3, 7) was supported by the Russian Science Foundation under grant no. 23-11-00143, https://rscf.ru/en/project/23-11-00143/, and performed at the Steklov Mathematical Institute of Russian Academy of Sciences. The work of Temurbek Rahmatullaev (Sections 4–6) was carried out within the project “Mirror Laboratories” at HSE University, Russian Federation.
Received: February 19, 2024
Revised: June 7, 2024
Accepted: June 11, 2024
English version:
Proceedings of the Steklov Institute of Mathematics, 2024, Volume 326, Pages 269–285
DOI: https://doi.org/10.1134/S0081543824040126
Bibliographic databases:
Document Type: Article
UDC: 515.14+512.54
Language: Russian
Citation: Taras E. Panov, Temurbek A. Rahmatullaev, “Polyhedral Products, Graph Products, and $p$-Central Series”, Topology, Geometry, Combinatorics, and Mathematical Physics, Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 326, Steklov Math. Inst., Moscow, 2024, 293–310; Proc. Steklov Inst. Math., 326 (2024), 269–285
Citation in format AMSBIB
\Bibitem{PanRah24}
\by Taras~E.~Panov, Temurbek~A.~Rahmatullaev
\paper Polyhedral Products, Graph Products, and $p$-Central Series
\inbook Topology, Geometry, Combinatorics, and Mathematical Physics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 326
\pages 293--310
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4425}
\crossref{https://doi.org/10.4213/tm4425}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=794845}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 326
\pages 269--285
\crossref{https://doi.org/10.1134/S0081543824040126}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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