A Class of Lie 2-Algebras in Higher-Order Courant Algebroids  

作　　者：Yanhui Bi Fengying Han Meili Sun Yanhui Bi;Fengying Han;Meili Sun(College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, China)

机构地区：[1]College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, China

出　　处：《Journal of Applied Mathematics and Physics》2016年第7期1254-1259,共6页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Higher-Order Courant Algebroids Higher-Order Dorfman Algebroids Lie 2-Algebra 

分 类 号：O22[理学—运筹学与控制论]