537 research outputs found
E-Courant algebroids
In this paper, we introduce the notion of -Courant algebroids, where
is a vector bundle. It is a kind of generalized Courant algebroid and contains
Courant algebroids, Courant-Jacobi algebroids and omni-Lie algebroids as its
special cases. We explore novel phenomena exhibited by -Courant algebroids
and provide many examples. We study the automorphism groups of omni-Lie
algebroids and classify the isomorphism classes of exact -Courant
algebroids. In addition, we introduce the concepts of -Lie bialgebroids and
Manin triples.Comment: 29 pages, no figur
Deformations of Lie 2-algebras
In this paper, we consider deformations of Lie 2-algebras via the cohomology
theory. We prove that a 1-parameter infinitesimal deformation of a Lie
2-algebra \g corresponds to a 2-cocycle of \g with the coefficients in the
adjoint representation. The Nijenhuis operator for Lie 2-algebras is introduced
to describe trivial deformations. We also study abelian extensions of Lie
2-algebras from the viewpoint of deformations of semidirect product Lie
2-algebras.Comment: 20 page
- …