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The Homology of the Lamplighter Lie Algebra

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Algebra and Logic Aims and scope

It is proved that the associated Lie algebra of the Mal’tsev ℚ-completion of the lamplighter group is the pronilpotent completion of the lamplighter Lie algebra. It is also shown that the homology of this completed Lie algebra is of uncountable dimension in each degree.

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References

  1. S. O. Ivanov and R. Mikhailov, “A finite ℚ-bad space,” Geom. Topol., 23, No. 3, 1237-1249 (2019).

    Article  MathSciNet  Google Scholar 

  2. S. O. Ivanov, R. Mikhailov, and A. Zaikovskii, “Homological properties of parafree Lie algebras,” J. Alg., 560, 1092-1106 (2020).

    Article  MathSciNet  Google Scholar 

  3. Y. Félix, S. Halperin, and J.-C. Thomas, Rational Homotopy Theory II, World Scientific, Hackensack, NJ (2015).

    Book  Google Scholar 

  4. A. I. Mal’tsev, “On a class of homogeneous spaces,” Izv. Akad. Nauk SSSR, Ser. Mat., 13, No. 1, 9-32 (1949).

    MathSciNet  MATH  Google Scholar 

  5. D. Quillen, “Rational homotopy theory,” Ann. Math. (2), 90, 205-295 (1969).

    Article  MathSciNet  Google Scholar 

  6. Y. Félix, S. Halperin, and J.-C. Thomas, Rational Homotopy Theory, Grad. Texts Math., 205, Springer, New York, NY (2001).

  7. J.-P. Serre, Lie Algebras and Lie Groups. 1964 Lectures Given at Harvard University, W. A. Benjamin, New York (1965).

  8. U. Buijs, Y. Félix, A. Murillo, and D. Tanré, Lie Models in Topology, Prog. Math., 335, Birkhäuser, Cham (2020).

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Authors and Affiliations

  1. Institut de Mathématiques et Physique, Université Catholique de Louvain, Louvain-la-Neuve, Belgique

    Y. Félix

  2. Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Málaga, Spain

    A. Murillo

Authors
  1. Y. Félix
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  2. A. Murillo
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Corresponding author

Correspondence to Y. Félix.

Additional information

Translated from Algebra i Logika, Vol. 60, No. 6, pp. 636-646, November-December, 2021. Russian DOI: https://doi.org/10.33048/alglog.2021.60.608.

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Félix, Y., Murillo, A. The Homology of the Lamplighter Lie Algebra. Algebra Logic 60, 425–432 (2022). https://doi.org/10.1007/s10469-022-09668-w

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  • DOI: https://doi.org/10.1007/s10469-022-09668-w

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