Quantizability conjecture for Lie bialgebroids
Let be a Lie algebroid, and suppose its dual bundle is also a Lie algebroid such that the differential on is a derivation of the super-bracket on . Call a Lie bialgebroid. It is quantizable if there exists a deformation of its universal enveloping algebra whose semi-classical limit is precisely the given Lie bialgebroid structure.
Quantizability conjecture. Any Lie bialgebroid is quantizable.
This asserts the existence of a deformation quantization for every Lie bialgebroid. The supplied text gives no evidence that the assertion has been proved or disproved, so its status remains open.
References
Primary source
Damien Calaque, “Formality for Lie algebroids”, arXiv:math/0404265 (2004).
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