论文标题
$ l _ {\ leqslant 3} $代数的内部对称性
Internal symmetry of the $L_{\leqslant 3}$ algebra arising from a Lie pair
论文作者
论文摘要
一对谎言对是一个包含$ a $ a $ to $ l $在同一基本歧管上。在较早的工作中，第三位作者，Bandiera，Stiénon和Xu引入了规范的$ l _ {\ leqslant 3} $ algebra $γ（\ wedge^\ bulter a^\ vee \ vee \ ootimes l/a）$ chevalley-eilenberggergnialbergnial a a a a a a a a a a）在本说明中，我们证明，对于这样的谎言对，在$ l _ {\ leqslant 3} $ algebra $γ（\ wedge^\ bulter a^\ vee a^\ vee \ otimes l/a）$上，有$ \ mathrm {der}（l）$相关的谎言代数动作。这里$ \ mathrm {der}（l）$是Lie代数$ l $或$ L $的无限型汽车上的派生空间。 The said action gives rise to a larger scope of gauge equivalences of Maurer-Cartan elements in $Γ(\wedge^\bullet A^\vee \otimes L/A)$, and for this reason we elect to call the $\mathrm{Der}(L)$-action internal symmetry of $Γ(\wedge^\bullet A^\vee \otimes L/A)$.
A Lie pair is an inclusion $A$ to $L$ of Lie algebroids over the same base manifold. In an earlier work, the third author with Bandiera, Stiénon, and Xu introduced a canonical $L_{\leqslant 3}$ algebra $Γ(\wedge^\bullet A^\vee \otimes L/A)$ whose unary bracket is the Chevalley-Eilenberg differential arising from every Lie pair $(L,A)$. In this note, we prove that to such a Lie pair there is an associated Lie algebra action by $\mathrm{Der}(L)$ on the $L_{\leqslant 3}$ algebra $Γ(\wedge^\bullet A^\vee \otimes L/A)$. Here $\mathrm{Der}(L)$ is the space of derivations on the Lie algebroid $L$, or infinitesimal automorphisms of $L$. The said action gives rise to a larger scope of gauge equivalences of Maurer-Cartan elements in $Γ(\wedge^\bullet A^\vee \otimes L/A)$, and for this reason we elect to call the $\mathrm{Der}(L)$-action internal symmetry of $Γ(\wedge^\bullet A^\vee \otimes L/A)$.
