 Special cases of generalized complex structures include complex structure and a version of Kähler structure which includes the B-field.In 1987 Irene Dorfman introduced the Dorfman bracket [,]D, which like the Courant bracket provides an integrability condition for Dirac structures.It is defined by

The Dorfman bracket is not antisymmetric, but it is often easier to calculate with than the Courant bracket because it satisfies a Leibniz rule which resembles the Jacobi identity

The Courant bracket does not satisfy the [[Jacobi identity]] and so it does not define a [[Lie algebroid]], in addition it fails to satisfy the Lie algebroid condition on the [[anchor map]].