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I got a complaint from the authors of the first reference (J. of Diff.geom. 1997), stating that Courant did not bother too much about axiomatizing his skew-bracket. Instead, the authors of the reference axiomatized the notion of what is now called Courant algebroid. I have corrected the introductory words accordingly. You can read the references in order to check the present accuracy.

Also it might be fair to mention I.Y. Dorfman parallel to J.T. Courant, because she invented the equivalent bracket (now called Dorfman bracket) on ${\displaystyle TM\oplus T^{*}M}$ to describe integrability of certain structures. MelchiorG ( talk) 06:11, 24 March 2012 (UTC) reply