abstract: We discuss the notion of basic cohomology for Dirac structures and, more generally, Lie algebroids. We then use this notion to characterize the obstruction to a variational formulation of Dirac dynamics.

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@article{Cosserat-On-Dirac-structures-2023,
 abstract = {We discuss the notion of basic cohomology for Dirac structures and, more
generally, Lie algebroids. We then use this notion to characterize the
obstruction to a variational formulation of Dirac dynamics.},
 author = {Cosserat, Oscar and Kotov, Alexei and Laurent-Gengoux, Camille and Ryvkin, Leonid and Salnikov, Vladimir},
 doi = {10.2140/memocs.2023.11.1},
 eprint = {2109.00313},
 fjournal = {Mathematics and Mechanics of Complex Systems},
 issn = {2326-7186},
 journal = {Math. Mech. Complex Syst.},
 keywords = {37J06,70H45,37J39,37J51,53D17,70H30},
 language = {English},
 number = {1},
 pages = {1--18},
 title = {On {Dirac} structures admitting a variational approach},
 volume = {11},
 year = {2023},
 zbl = {1532.37051},
 zbmath = {7772345}
}