Homotopical rigidity of the pre-Lie operad

Dotsenko, Vladimir; Khoroshkin, Anton

doi:10.1090/proc/15627

Homotopical rigidity of the pre-Lie operad
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by Vladimir Dotsenko and Anton Khoroshkin

Proc. Amer. Math. Soc. 152 (2024), 1355-1371

DOI: https://doi.org/10.1090/proc/15627

Published electronically: February 14, 2024

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Abstract:

We show that the celebrated operad of pre-Lie algebras is very rigid: it has no “non-obvious” degrees of freedom from either of the three points of view: deformations of maps to and from the “three graces of operad theory”, homotopy automorphisms, and operadic twisting. Examining the latter, it is possible to answer two questions of Markl from 2005 [Czechoslovak Math. J. 57 (2007), pp. 253–268; J. Lie Theory 17 (2007), pp. 241–261], including a Lie-theoretic version of the Deligne conjecture.

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