A Class of Lie 2-Algebras in Higher-Order Courant Algebroids ()
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.
Share and Cite:
Bi, Y. , Han, F. and Sun, M. (2016) A Class of Lie 2-Algebras in Higher-Order Courant Algebroids.
Journal of Applied Mathematics and Physics,
4, 1254-1259. doi:
10.4236/jamp.2016.47131.
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