HOMOTOPICAL RIGIDITY OF THE PRE-LIE OPERAD

Vladimir Dotsenko; Anton Khoroshkin

doi:10.1090/proc/15627

HOMOTOPICAL RIGIDITY OF THE PRE-LIE OPERAD

Vladimir Dotsenko, Anton Khoroshkin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1355-1371
Number of pages	17
Journal	Proceedings of the American Mathematical Society
Volume	152
Issue number	4
DOIs	https://doi.org/10.1090/proc/15627
State	Published - 1 Apr 2024

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© 2024 American Mathematical Society. All rights reserved.

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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HOMOTOPICAL RIGIDITY OF THE PRE-LIE OPERAD

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