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Title: Structure of classical affine and classical affine fractional W-algebras

Abstract

We introduce a classical BRST complex (See Definition 3.2.) and show that one can construct a classical affine W-algebra via the complex. This definition clarifies that classical affine W-algebras can be considered as quasi-classical limits of quantum affine W-algebras. We also give a definition of a classical affine fractional W-algebra as a Poisson vertex algebra. As in the classical affine case, a classical affine fractional W-algebra has two compatible λ-brackets and is isomorphic to an algebra of differential polynomials as a differential algebra. When a classical affine fractional W-algebra is associated to a minimal nilpotent, we describe explicit forms of free generators and compute λ-brackets between them. Provided some assumptions on a classical affine fractional W-algebra, we find an infinite sequence of integrable systems related to the algebra, using the generalized Drinfel’d and Sokolov reduction.

Authors:
 [1]
  1. Department of Mathematical Sciences, Seoul National University, GwanAkRo 1, Gwanak-Gu, Seoul 151-747 (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, E-mail: uhrisu1@math.snu.ac.kr. Structure of classical affine and classical affine fractional W-algebras. United States: N. p., 2015. Web. doi:10.1063/1.4906144.
Suh, Uhi Rinn, E-mail: uhrisu1@math.snu.ac.kr. Structure of classical affine and classical affine fractional W-algebras. United States. doi:10.1063/1.4906144.
Suh, Uhi Rinn, E-mail: uhrisu1@math.snu.ac.kr. Thu . "Structure of classical affine and classical affine fractional W-algebras". United States. doi:10.1063/1.4906144.
@article{osti_22403077,
title = {Structure of classical affine and classical affine fractional W-algebras},
author = {Suh, Uhi Rinn, E-mail: 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 W-algebra via the complex. This definition clarifies that classical affine W-algebras can be considered as quasi-classical limits of quantum affine W-algebras. We also give a definition of a classical affine fractional W-algebra as a Poisson vertex algebra. As in the classical affine case, a classical affine fractional W-algebra has two compatible λ-brackets and is isomorphic to an algebra of differential polynomials as a differential algebra. When a classical affine fractional W-algebra is associated to a minimal nilpotent, we describe explicit forms of free generators and compute λ-brackets between them. Provided some assumptions on a classical affine fractional W-algebra, 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 = {Thu Jan 15 00:00:00 EST 2015},
month = {Thu Jan 15 00:00:00 EST 2015}
}