Remarks on the definition of a Courant algebroid. (English) Zbl 0999.22004

Uchino, Kyousuke

Lett. Math. Phys. 60, No. 2, 171-175 (2002).

The notion of a Courant algebroid was introduced by Zh. Liu, A. Weinstein and P. Xu [J. Differ. Geom. 45, 547-574 (1997; Zbl 0885.58030)] using five axioms and a defining relation for a derivation. In this paper it is shown that two of the axioms and the relation (assuming only the Leibniz rule) follow from the rest of the axioms.

Reviewer: Constantin Udrişte (Bucureşti)

MSC:

22A22	Topological groupoids (including differentiable and Lie groupoids)
17B62	Lie bialgebras; Lie coalgebras
53D17	Poisson manifolds; Poisson groupoids and algebroids

Keywords:

Lie bialgebras; Poisson manifolds; Courant algebroid

Citations:

Zbl 0885.58030