Infinitesimal symmetries of bundle gerbes and Courant algebroids

Pub Date : 2024-02-26 DOI:10.1007/s10711-024-00897-0

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Abstract

Let M be a smooth manifold and let \(\chi \in \Omega ^3(M)\) be closed differential form with integral periods. We show the Lie 2-algebra \(\mathbb {L}(C_\chi )\) of sections of the \(\chi \) -twisted Courant algebroid \(C_\chi \) on M is quasi-isomorphic to the Lie 2-algebra of connection-preserving multiplicative vector fields on an \(S^1\) -bundle gerbe with connection (over M) whose 3-curvature is \(\chi \) .

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束根和库朗梯形的无限对称性

Abstract Let M be a smooth manifold and let \(\chi \in \Omega ^3(M)\) be closed differential form with integral periods.我们证明在M上的\(\chi \) -twisted Courant algebroid \(C_\chi \)的截面的Lie 2-代数（\mathbb {L}(C_\chi )）与3-曲率为\(\chi \)的\(S^1\) -bundle gerbe with connection (over M)上的连接保留乘法向量场的Lie 2-代数准同构。

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