**The International Conference on
**

Secondary Calculus and Cohomological Physics,

Moscow, August 24 - August 31, 1997

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Courant algebroids and strongly homotopy Lie algebras

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Dmitry Roytenberg, Alan Weinstein

University of California at Berkeley, Berkeley, California E-mail: roytenbe@math.berkeley.edu University of California at Berkeley, Berkeley, California E-mail: alanw@math.berkeley.edu

**Abstract:** Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the bundle $TM\oplus T^*M$ with the bracket introduced by T. Courant for the study of Dirac structures. Within the category of Courant algebroids one can construct the doubles of Lie bialgebroids, the infinitesimal objects for Poisson groupoids. We show that Courant algebroids can be considered as strongly homotopy Lie algebras.

**Keywords:** Dirac structures, Lie algebroids, homotopy Lie algebras

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