Abstract We give a self-contained survey of some approaches aimed at global description the geometry underlying double field theory. After reviewing Courant algebroids and their incarnations in AKSZ construction, we develop theory metric including graded geometry. use to doubled geometry, incorporating section constraint, as well an AKSZ-type construction topological sigma-models. When these no...

In this paper we discuss the relation between the unimodularity of a Lie algebroid τA : A → Q and the existence of invariant volume forms for the hamiltonian dynamics on the dual bundle A. The results obtained in this direction are applied to several hamiltonian systems on different examples of Lie algebroids.

In this paper we propose a new algorithm for obtaining the rational integrals of the full Kostant–Toda lattice. This new approach is based on a reduction of a bi-Hamiltonian system on gl(n,R). This system was obtained by reducing the space of maps from Zn to GL(n,R) endowed with a structure of a pair of Lie-algebroids.

This paper is a companion to the Boardman–Wilson paper on the ring spectrum P (n). When the prime is 2, this spectrum is not commutative, which introduces several complications. Here, we supply the necessary details of the relevant Hopf algebroids and Hopf ring for this case.