Journal of Applied Mathematics and Physics

Volume 4, Issue 7 (July 2016)

ISSN Print: 2327-4352   ISSN Online: 2327-4379

Google-based Impact Factor: 0.70  Citations  

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

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DOI: 10.4236/jamp.2016.47131    1,203 Downloads   1,998 Views  

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 TMpT*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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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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