Quantum Toroidal Comodule Algebra of Type An−1 and Integrals of Motion

Boris Feigin; Michio Jimbo; Evgeny Mukhin

doi:10.3842/SIGMA.2022.051

Quantum Toroidal Comodule Algebra of Type A_n−1 and Integrals of Motion

Boris Feigin, Michio Jimbo, Evgeny Mukhin

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce an algebra K_n which has a structure of a left comodule over the quantum toroidal algebra of type A_n−1. Algebra K_n is a higher rank generalization of K₁, which provides a uniform description of deformed W algebras associated with Lie (super)al-gebras of types BCD. We show that K_n possesses a family of commutative subalgebras.

Original language	English
Article number	051
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	18
DOIs	https://doi.org/10.3842/SIGMA.2022.051
State	Published - 2022
Externally published	Yes

Keywords

comodule
integrals of motion
quantum toroidal algebras

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Geometry and Topology

Access to Document

10.3842/SIGMA.2022.051

Cite this

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title = "Quantum Toroidal Comodule Algebra of Type An−1 and Integrals of Motion",

abstract = "We 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)al-gebras of types BCD. We show that Kn possesses a family of commutative subalgebras.",

keywords = "comodule, integrals of motion, quantum toroidal algebras",

author = "Boris Feigin and Michio Jimbo and Evgeny Mukhin",

year = "2022",

doi = "10.3842/SIGMA.2022.051",

language = "الإنجليزيّة",

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publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

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AU - Feigin, Boris

AU - Jimbo, Michio

AU - Mukhin, Evgeny

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AB - We 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)al-gebras of types BCD. We show that Kn possesses a family of commutative subalgebras.

KW - comodule

KW - integrals of motion

KW - quantum toroidal algebras

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DO - 10.3842/SIGMA.2022.051

M3 - مقالة

SN - 1815-0659

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JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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