This paper is devoted to studying some properties of the Courant. algebroids: we explain the so-called "conducting bundle construction" and use it to attach the Courant algebroid to the Dixmier-Douady gerbe (following the ideas of P. Severa). We note that the WZNW-Poisson condition of Klimcik and Strobl (math.SG/0104189) is the same as the Dirac structure in some particular Courant algebroid. We propose the construction of the Lie algebroid on the loop space starting from the Lie algebroid on the manifold and conjecture that this construction applied to this Dirac structure should give the Lie algebroid of symmetries in the WZNW-Poisson σ-model and show that it is indeed true in the particular case of the Poisson cr-model.
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