TITLE:
A Class of Lie 2-Algebras in Higher-Order Courant Algebroids
AUTHORS:
Yanhui Bi, Fengying Han, Meili Sun
KEYWORDS:
Higher-Order Courant Algebroids, Higher-Order Dorfman Algebroids, Lie 2-Algebra
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.7,
July
22,
2016
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*Mfor
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.