Classical \(\mathcal W\)-algebras in types \(A\), \(B\), \(C\), \(D\) and \(G\)
type: Item
instance of: scholarly article
title: Classical \(\mathcal W\)-algebras in types \(A\), \(B\), \(C\), \(D\) and \(G\)
zbMATH Open document ID: 1321.17020
published in: Communications in Mathematical Physics
publication date: 2015-04-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1403.1700
review text: In this paper the authors propose an explicit generating system for the classical \(\mathcal{W}\)-algebras associated to the principal nilpotent elements in types \(A\), \(B\), \(C\), \(D\) and \(G\). These generators are given as certain determinants of matrices formed by elements of differential algebras associated with the underlying Lie algebra, thus producing a realization in the context of Poisson vertex algebras. Additionally, it is shown that the image of these generators under the Chevalley-type projection coincide with the elements defined via the corresponding Miura transformation. This projection yields an isomorphism of Chevalley type to an algebra of polynomials defined as the intersection of the kernels of screening operators, providing a connection to the Harish-Chandra image of the Feigin-Frenkel center.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B69
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 17B35
zbMATH DE Number: 6424626
zbMATH Keywords: W-algebra
zbMATH Keywords: generator
zbMATH Keywords: Lie algebra
zbMATH Keywords: nilpotent element
zbMATH Keywords: determinant
zbMATH Keywords: Poisson vertex algebra
author: Alexander Molev
author: E. Ragoucy
MaRDI profile type: Publication
OpenAlex ID: W1605116455
arXiv ID: 1403.1700
cites work: Lie algebras and equations of Korteweg-de Vries type
cites work: Explicit generators in rectangular affine \(\mathcal {W}\)-algebras of type \(A\)
cites work: Extensions of the Virasoro algebra constructed from Kac-Moody algebras using higher order Casimir invariants
cites work: On Higher-Order Sugawara Operators
cites work: KZ equation, G-opers, quantum Drinfeld-Sokolov reduction, and quantum Cayley-Hamilton identity
cites work: Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras
cites work: On classical finite and affine W-algebras
cites work: Generalized Toda theories and \(\mathcal W\)-algebras associated with integral gradings
cites work: Folding the \(W\) algebras
cites work: Q5308978
cites work: Q4002278
cites work: Feigin-Frenkel center in types \(B\), \(C\) and \(D\)
cites work: Noncommutative symmetric functions
cites work: Q4040877
cites work: Q5687564
cites work: Modifying Lax equations and the second Hamiltonian structure
cites work: Two-dimensional exactly and completely integrable dynamical systems
cites work: Yangian Characters and Classical $$\mathcal{W}$$ -Algebras
cites work: Q4795286
DOI: 10.1007/S00220-014-2239-Y
Recommended article: Classical \(W\)-algebras
Recommended article: On classical finite and affine W-algebras
Recommended article: Structure of classical (finite and affine) \(\mathcal W\)-algebras
Recommended article: ON THE CLASSICAL WN(l) ALGEBRAS
Recommended article: Higher dimensional classical \(W\)-algebras
Recommended article: Q4872872
Recommended article: Classical \(\mathcal{W}\)-algebras for centralizers
Recommended article: Classical W-algebras within the theory of Poisson vertex algebras
Recommended article: Algebraic classical \(W\)-algebras and Frobenius manifolds
Recommended article: Q4233047
description: scientific article