Abstract
Protobialgebroids include several kinds of algebroid structures such as Lie algebroid, Lie bialgebroid, Lie quasi-bialgebroid, etc. In this paper, the Dirac theories are generalized from Lie bialgebroid to protobialgebroid. We give the integrable conditions for a maximally isotropic subbundle being a Dirac structure for a protobialgebroid by the notion of a characteristic pair. From the integrable conditions, we found out that the Dirac structure has closed relations with the twisting of a protobialgebroid. At last, some special cases of the Dirac structures for protobialgebroids are discussed.
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