Contact Courant algebroids and L_∞-algebras

2018/12/27 by Apurba Das, Das, Apurba
Mathematics · Physics and Astronomy · #53C15 #53D10 #53D35 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Rings and Algebras (math.RA) #math-ph #math.DG #math.MP #math.RA #msc:53C15 #msc:53D10 #msc:53D35

paper · pdf · doi:10.48550/arxiv.1901.00364

19 pages, comments are welcome

arxiv created 2018/12/27 · arxiv updated 2019/01/03

Abstract

Let L be a line bundle over M. In this paper we associate an L_∞-algebra to any L-Courant algebroid (contact Courant algebroid in the sense of Grabowski). This construction is similar to the work of Roytenberg and Weinstein for Courant algebroids. Next we associate a p-term L_∞-algebra to any isotropic involutive subbundle of (\mathbbDL)^p := DL ⊕ (\wedge^p (DL)^* ⊗ L), where DL is the gauge algebroid of L. In a particular case, we relate these L_∞-algebras by a suitable morphism.

Related

• L_∞-morphisms between twisted Courant r-Lie algebras and untwisted Courant (r+1)-Lie algebroids
• The Chern-Weil-Lecomte characteristic map for L_∞-algebras
• L_∞-actions of Lie algebroids
• LA-Courant algebroids and their applications
• An Introduction to L_∞-Algebras and their Homotopy Theory