Quantizability conjecture for Lie bialgebroids
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.
Sources & referencesView supporting material
Primary source
Damien Calaque, “Formality for Lie algebroids”, arXiv:math/0404265 (2004).
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