# -Operators on Lie ∞-algebras with respect to Lie ∞-actions

@article{Caseiro2022OperatorsOL,
title={-Operators on Lie ∞-algebras with respect to Lie ∞-actions},
author={Raquel Caseiro and J.M. Nunes da Costa},
journal={Communications in Algebra},
year={2022},
volume={50},
pages={3079 - 3101}
}
• Published 3 September 2021
• Mathematics
• Communications in Algebra
Abstract We define -operators on a Lie ∞-algebra E with respect to an action of E on another Lie ∞-algebra and we characterize them as Maurer-Cartan elements of a certain Lie ∞-algebra obtained by Voronov’s higher derived brackets construction. The Lie ∞-algebra that controls the deformation of -operators with respect to a fixed action is determined.
1 Citations

## References

SHOWING 1-10 OF 20 REFERENCES
Lie theory for nilpotent L∞-algebras
The Deligne groupoid is a functor from nilpotent differential graded Lie algebras concentrated in positive degrees to groupoids; in the special case of Lie algebras over a field of characteristic
Deformations and Homotopy Theory of Relative Rota–Baxter Lie Algebras
• Mathematics
Communications in Mathematical Physics
• 2020
We determine the $$L_\infty$$ L ∞ -algebra that controls deformations of a relative Rota–Baxter Lie algebra and show that it is an extension of the dg Lie algebra controlling deformations of
Strongly homotopy Lie algebras
• Mathematics
• 1994
The present paper can be thought of as a continuation of the paper "Introduction to sh Lie algebras for physicists" by T. Lada and J. Stasheff (International Journal of Theoretical Physics Vol. 32,
Introduction to SH Lie algebras for physicists
• Mathematics
• 1993
UNC-MATH-92/2originally April 27, 1990, revised September 24, 1992INTRODUCTION TO SH LIE ALGEBRAS FOR PHYSICISTSTom LadaJim StasheffMuch of point particle physics can be described in terms of Lie
What a Classical r-Matrix Really Is
Abstract To my friend and colleague K.C. Reddy on occasion of his retirement. The notion of classical r-matrix is re-examined, and a definition suitable to differential (-difference) Lie algebras, –
AN ANALYTIC PROBLEM WHOSE SOLUTION FOLLOWS FROM A SIMPLE ALGEBRAIC IDENTITY
After integrating both sides of the equation in (1.1) and using the notation of (1.3), we find that (1.4) y = l + Hφy) has the solution (1.5) y = exp (Xφ) = 1 + Xφ + Xφl2l + λ^/3! + • By the method
L∞-algebra actions. Differential Geometry and its Applications
• 2012
L∞-algebra actions
• Mathematics
• 2012