A Class of Lie 2-Algebras in Higher-Order Courant Algebroids ()
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ABSTRACT
In this paper, we study the relation of the algebraic properties of the higher-order Courant bracket and Dorfman bracket on the direct sum bundle TM⊕∧pT*M for an m-dimensional smooth manifold M, and a Lie 2-algebra which is a “categorified” version of a Lie algebra. We prove that the higher-order Courant algebroids give rise to a semistrict Lie 2-algebra, and we prove that the higher-order Dorfman algebroids give rise to a hemistrict Lie 2-algebra. Consequently, there is an isomorphism from the higher-order Courant algebroids to the higher-order Dorfman algebroids as Lie 2-algebras homomorphism.
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