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- W3102040445 abstract "Li-Bland's correspondence between linear Courant algebroids and Lie $2$-algebroids is explained and shown to be an equivalence of categories. Decomposed VB-Courant algebroids are shown to be equivalent to split Lie 2-algebroids in the same manner as decomposed VB-algebroids are equivalent to 2-term representations up to homotopy (Gracia-Saz and Mehta). Several classes of examples are discussed, yielding new examples of split Lie 2-algebroids. We prove that the bicrossproduct of a matched pair of $2$-representations is a split Lie $2$-algebroid and we explain this result geometrically, as a consequence of the equivalence of VB-Courant algebroids and Lie $2$-algebroids. This explains in particular how the two notions of double of a matched pair of representations are geometrically related. In the same manner, we explain the geometric link between the two notions of double of a Lie bialgebroid." @default.
- W3102040445 created "2020-11-23" @default.
- W3102040445 creator A5017722073 @default.
- W3102040445 date "2019-09-16" @default.
- W3102040445 modified "2023-10-16" @default.
- W3102040445 title "Lie 2-algebroids and matched pairs of 2-representations : a geometric approach" @default.
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- W3102040445 doi "https://doi.org/10.2140/pjm.2019.301.143" @default.
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