# Integrals of motion and quantum groups

@article{Feigin1993IntegralsOM, title={Integrals of motion and quantum groups}, author={Boris Feigin and Edward Frenkel}, journal={Lecture Notes in Mathematics}, year={1993}, volume={1620}, pages={349-418} }

A homological construction of integrals of motion of the classical and quantum Toda field theories is given. Using this construction, we identify the integrals of motion with cohomology classes of certain complexes, which are modeled on the BGG resolutions of the associated Lie algebras and their quantum deformations. This way we prove that all classical integrals of motion can be quantized. For the Toda field theories associated to finite-dimensional Lie algebras, the algebra of integrals of…

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