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arXiv · 2409.05041

Stability and rigidity of 3-Lie algebra morphisms

Jun Jiang·Yunhe Sheng·Geyi Sun
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Abstract

In this paper, first we use the higher derived brackets to construct an $L_\infty$-algebra, whose Maurer-Cartan elements are $3$-Lie algebra morphisms. Using the differential in the $L_\infty$-algebra that govern deformations of the morphism, we give the cohomology of a $3$-Lie algebra morphism. Then we study the rigidity and stability of $3$-Lie algebra morphisms using the established cohomology theory. In particular, we show that if the first cohomology group is trivial, then the morphism is rigid; if the second cohomology group is trivial, then the morphism is stable. Finally, we study the stability of $3$-Lie subalgebras similarly.

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Jun Jiang, Yunhe Sheng, Geyi Sun. 2024-09-08. Stability and rigidity of 3-Lie algebra morphisms. https://doi.org/10.1016/j.difgeo.2025.102278

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