Structure of classical affine and classical affine fractional Walgebras
Abstract
We introduce a classical BRST complex (See Definition 3.2.) and show that one can construct a classical affine Walgebra via the complex. This definition clarifies that classical affine Walgebras can be considered as quasiclassical limits of quantum affine Walgebras. We also give a definition of a classical affine fractional Walgebra as a Poisson vertex algebra. As in the classical affine case, a classical affine fractional Walgebra has two compatible λbrackets and is isomorphic to an algebra of differential polynomials as a differential algebra. When a classical affine fractional Walgebra is associated to a minimal nilpotent, we describe explicit forms of free generators and compute λbrackets between them. Provided some assumptions on a classical affine fractional Walgebra, we find an infinite sequence of integrable systems related to the algebra, using the generalized Drinfel’d and Sokolov reduction.
 Authors:
 Department of Mathematical Sciences, Seoul National University, GwanAkRo 1, GwanakGu, Seoul 151747 (Korea, Republic of)
 Publication Date:
 OSTI Identifier:
 22403077
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; INTEGRAL CALCULUS; POLYNOMIALS; REDUCTION
Citation Formats
Suh, Uhi Rinn, Email: uhrisu1@math.snu.ac.kr. Structure of classical affine and classical affine fractional Walgebras. United States: N. p., 2015.
Web. doi:10.1063/1.4906144.
Suh, Uhi Rinn, Email: uhrisu1@math.snu.ac.kr. Structure of classical affine and classical affine fractional Walgebras. United States. doi:10.1063/1.4906144.
Suh, Uhi Rinn, Email: uhrisu1@math.snu.ac.kr. 2015.
"Structure of classical affine and classical affine fractional Walgebras". United States.
doi:10.1063/1.4906144.
@article{osti_22403077,
title = {Structure of classical affine and classical affine fractional Walgebras},
author = {Suh, Uhi Rinn, Email: uhrisu1@math.snu.ac.kr},
abstractNote = {We introduce a classical BRST complex (See Definition 3.2.) and show that one can construct a classical affine Walgebra via the complex. This definition clarifies that classical affine Walgebras can be considered as quasiclassical limits of quantum affine Walgebras. We also give a definition of a classical affine fractional Walgebra as a Poisson vertex algebra. As in the classical affine case, a classical affine fractional Walgebra has two compatible λbrackets and is isomorphic to an algebra of differential polynomials as a differential algebra. When a classical affine fractional Walgebra is associated to a minimal nilpotent, we describe explicit forms of free generators and compute λbrackets between them. Provided some assumptions on a classical affine fractional Walgebra, we find an infinite sequence of integrable systems related to the algebra, using the generalized Drinfel’d and Sokolov reduction.},
doi = {10.1063/1.4906144},
journal = {Journal of Mathematical Physics},
number = 1,
volume = 56,
place = {United States},
year = 2015,
month = 1
}

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