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Item Quantum Toroidal Comodule Algebra of Type A(n-1) and Integrals of Motion(Foundation Compositio Mathematica, 2022-07-07) Feigin, Boris; Jimbo, Michio; Mukhin, Evgeny; Mathematical Sciences, School of ScienceWe introduce an algebra Kn which has a structure of a left comodule over the quantum toroidal algebra of type An−1. Algebra Kn is a higher rank generalization of K1, which provides a uniform description of deformed W algebras associated with Lie (super)algebras of types BCD. We show that Kn possesses a family of commutative subalgebras.