Deformation maps on quasi-twilled Lie conformal algebras
Abstract
In this paper, we develop a unified approach for various operators on Lie conformal algebras. Given a quasi-twilled Lie conformal algebra (Ep,Vs,Ws), we introduce two dual families of operators: \emph{right deformation maps} D:Vs→Ws and \emph{left deformation maps} B:Ws→Vs. Each family simultaneously subsumes several classical structures: modified r-matrices, crossed homomorphisms, derivations, and Lie conformal algebra homomorphisms in the right case, relative Rota-Baxter operators, twisted Rota-Baxter operators, Reynolds operators, and deformation maps of matched pairs in the left case. Using Voronov's derived bracket method, we construct the controlling homotopy algebras: a curved L∞-algebra governing right deformation maps and an L∞-algebra governing left deformation maps, with Maurer-Cartan elements precisely characterizing each type. We further develop the associated deformation theories via twisted L∞-algebras and define cohomology complexes for both types of deformation maps, recovering and extending the cohomologies of all classical and conformal operators already developed in the literature.
Related
- Diassociative conformal algebras and their deformation cohomology
- Markov maps and quasi-conformal deformations associated to geometrically finite Kleinian groups
- The index of conformal Hopf maps
- Deformation theory and the controlling L∞-structure of extended Rota-Baxter algebras
- Harmonic-Einstein maps and critical metrics for eigenvalues of the conformal Laplacian
BibTeX
@misc{chtioui2026deformation,
title = {{Deformation maps on quasi-twilled Lie conformal algebras}},
author = {Taoufik Chtioui and Sami Mabrouk and Abdenacer Makhlouf},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.28825},
eprint = {2606.28825},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.28825},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Deformation maps on quasi-twilled Lie conformal algebras
AU - Taoufik Chtioui
AU - Sami Mabrouk
AU - Abdenacer Makhlouf
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2606.28825
UR - https://arxiv.org/abs/2606.28825
AB - In this paper, we develop a unified approach for various operators on Lie conformal algebras. Given a quasi-twilled Lie conformal algebra (Ep,Vs,Ws), we introduce two dual families of operators: \emph{right deformation maps} D:Vs→Ws and \emph{left deformation maps} B:Ws→Vs. Each family simultaneously subsumes several classical structures: modified r-matrices, crossed homomorphisms, derivations, and Lie conformal algebra homomorphisms in the right case, relative Rota-Baxter operators, twisted Rota-Baxter operators, Reynolds operators, and deformation maps of matched pairs in the left case. Using Voronov's derived bracket method, we construct the controlling homotopy algebras: a curved L_∞-algebra governing right deformation maps and an L_∞-algebra governing left deformation maps, with Maurer-Cartan elements precisely characterizing each type. We further develop the associated deformation theories via twisted L_∞-algebras and define cohomology complexes for both types of deformation maps, recovering and extending the cohomologies of all classical and conformal operators already developed in the literature.
ER -