Abstract
We study the lower central series of a right-angled Coxeter group \({\rm{R}}{{\rm{C}}_{\cal K}}\) and the associated graded Lie algebra \(L\left( {{\rm{R}}{{\rm{C}}_{\cal K}}} \right)\). The latter is related to the graph Lie algebra \({L_{\cal K}}\). We give an explicit combinatorial description of the first three consecutive factors of the lower central series of the group \({\rm{R}}{{\rm{C}}_{\cal K}}\).
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Acknowledgments
I express my gratitude to my supervisor Taras Evgenievich Panov for the statement of the problem, help, and advice.
Funding
The work was supported by the Russian Foundation for Basic Research, project nos. 16-51-55017 and 17-01-00671.
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Dedicated to Victor Matveevich Buchstaber on the occasion of his 75th birthday
This article was submitted by the author simultaneously in Russian and English
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Vol. 305, pp. 61–70.
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Veryovkin, Y.A. The Associated Lie Algebra of a Right-Angled Coxeter Group. Proc. Steklov Inst. Math. 305, 53–62 (2019). https://doi.org/10.1134/S0081543819030040
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DOI: https://doi.org/10.1134/S0081543819030040