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In this paper, we show that the Jacobiator J of a pre-Courant algebroid is closed naturally. The corresponding equivalence class [J♭] is defined as the Pontryagin class, which is the obstruction of a pre-Courant algebroid to be deformed into a Courant algebroid. We construct a Leibniz 2-algebra and a Lie 2-algebra associated to a pre-Courant algebroid and prove that these algebraic structures are...
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