In this section we apply a recent striking result of M. Weiss [Wei16] to exhibit examples where the conditions of Theorem 3 are satisfied. As a byproduct we will obtain a proof of Theorem 1.
By a Lie pair (L,A), we mean an ordinary (non-graded) Lie algebroid (L,[⋅,⋅]L,ρL) over an ordinary (non-graded) smooth manifold M, together with a Lie subalgebroid (A,[⋅,⋅]A,ρA) of L over the same base M.
Z. Chen would like to thank P. Xu and M. Stienon for the useful discussions and suggestions that helped him improving this work. Y.-H. Sheng gives his warmest thanks to L. Hoevenaars, M. Crainic, I. Moerdijk and C. Zhu for their help and useful comm…
To prove Proposition 3.2 and Theorem 3.3, we essentially follow Ramadoss’s approach . Let L(D1poly) be the (graded) free Lie algebra generated over R by D1poly concentrated in degree 1. In other words, L(D1poly) is the smallest Lie subalgebra of …
Throughout this section, (Θ\lx@stackrelΦ→G) denotes a Lie group crossed module, and G⋉Θ its associated Lie 2-group. By (θ\lx@stackrelϕ→g), we denote its corresponding Lie algebra crossed module, and by g⋉θ the semidirect product Lie algebra.
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