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Owen Lynch (Feb 19 2022 at 18:25):Apparently the general setting for Dirac structures is "Courant Algebroids"
https://link.springer.com/content/pdf/10.1007/s00332-009-9052-3.pdf
Owen Lynch (Feb 19 2022 at 18:26):
John Baez (Feb 20 2022 at 00:46):This is getting suspiciously similar to the stuff I used to do on higher gauge theory!
John Baez (Feb 20 2022 at 00:46):Back then I would talk to Courant algebroid experts.
John Baez (Feb 20 2022 at 00:47):You should probably peek at the nLab to get Urs Schreiber's take on Courant algebroids.
Owen Lynch (Feb 20 2022 at 01:20):nLab says that a Courant algebroid is a symplectic Lie 2-algebroid... which sounds right up your alley!
Owen Lynch (Feb 20 2022 at 15:09):I've definitely stumbled back into your backyard: I'm now reading your paper on Lie 2-algebras
John Baez (Feb 20 2022 at 15:14):Great!