Higher Multi-Courant Algebroids

Abstract

The binary bracket of a Courant algebroid structure on $(E,⟨\cdot ,\cdot ⟩)$ can be extended to a $n$-ary bracket on $\Gamma (E)$, yielding a multi-Courant algebroid. These $n$-ary brackets form a Poisson algebra and were defined, in an algebraic setting, by Keller and Waldmann. We construct a higher geometric version of Keller-Waldmann Poisson algebra and define higher multi-Courant algebroids. As Courant algebroid structures can be seen as degree $3$ functions on a graded symplectic manifold of degree $2$, higher multi-Courant structures can be seen as functions of degree $n\ge 3$ on that graded symplectic manifold.

20 pages, to appear in Journal of Geometry and Physics

References in corpus (1)

• Courant cohomology, Cartan calculus, connections, curvature, characteristic classes