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Communications in Algebra Volume 50, 2022 - Issue 9
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Articles

Linking of letters and the lower central series of free groups

Jeff MonroeMathematics Department, University of Oregon, Eugene, OR, USA
&
Dev SinhaMathematics Department, University of Oregon, Eugene, OR, USACorrespondence[email protected]
Pages 3678-3703 | Received 30 Dec 2020, Accepted 12 Jan 2022, Published online: 08 Mar 2022

References

  • Bokut, L., Chibrikov, E. S. (2006). Lyndon-Shirshov words, Gröbner-Shirshov bases, and free Lie algebras. In: Non-associative algebra and its applications, volume 246 of Lect. Notes Pure Appl. Math. Boca Raton, FL: Chapman & Hall/CRC, pp. 17–39.
  • Buijs, U., Félix, Y., Murillo, A., Tanré, D. (2018). Homotopy theory of complete Lie algebras and Lie models of simplicial sets. J. Topol. 11(3):799–825. DOI: 10.1112/topo.12073.
  • Chibrikov, E. S. (2006). A right normed basis for free Lie algebras and Lyndon-Shirshov words. J. Algebra 302(2):593–612. DOI: 10.1016/j.jalgebra.2006.03.036.
  • Chen, K. T., Fox, R. H., Lyndon, R. C. (1958). Free differential calculus, iv. the quotient groups of the lower central series. Ann. Math. 68(1):81–95. DOI: 10.2307/1970044.
  • Fox, R. (1953). Free differential calculus, I: Derivation in the free group ring. Ann. Math. 57(3):547–560.
  • Lawrence, R., Sullivan, D. (2014). A formula for topology/deformations and its significance. Fund. Math. 225(1):229–242. DOI: 10.4064/fm225-1-10.
  • Magnus, W. (1940). Über gruppen und zugeordnete liesche ringe. J. Reine Angew. Math. 182:142–149.
  • Melancon, G., Reutenauer, C. (1996). Free lie superalgebras, trees and chains of partitions. J. Algebraic Combin. 5(4):337–351. DOI: 10.1007/BF00193184.
  • Milnor, J. (1954). Link groups. Ann. Math. 59(2):177–195. DOI: 10.2307/1969685.
  • Reutenauer, C. (1993). Free Lie algebras, volume 7 of London Mathematical Society Monographs. New Series. New York: Oxford Science Publications/The Clarendon Press, Oxford University Press.
  • Sinha, D. (2005). A pairing between graphs and trees. math/0502547.
  • Sinha, D., Walter, B. (2011). Lie coalgebras and rational homotopy theory, I: graph coalgebras. Homology Homotopy Appl. 13(2):263–292.
  • Sinha, D., and Walter, B. (2013). Lie coalgebras and rational homotopy theory II: Hopf invariants. Trans. Amer. Math. Soc. 365(2):861–883.
  • Sinha, D. P. (2013). The (non-equivariant) homology of the little disks operad. In OPERADS 2009, volume 26 of Sémin. Congr. France, Paris: Soc. Math., pp. 253–279.
  • Walter, B. (2010). Free lie algebras via the configuration pairing. arXiv:1010.4732.
  • Walter, B., Shiri, A. (2016). The left greedy Lie algebra basis and star graphs. Involve 9(5):783–795. DOI: 10.2140/involve.2016.9.783.

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