A class of W-algebras with infinitely generated classical limit

J. de Boer, L. Fehér, A. Honecker

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Abstract

There is a relatively well understood class of deformable W-algebras, resulting from Drinfeld-Sokolov (DS) type reductions of Kac-Moody algebras, which are Poisson bracket algebras based on finitely, freely generated rings of differential polynomials in the classical limit. The purpose of this paper is to point out the existence of a second class of deformable W-algebras, which in the classical limit are Poisson bracket algebras carried by infinitely, nonfreely generated rings of differential polynomials. We present illustrative examples of coset constructions, orbifold projections, as well as first class hamiltonian reductions of DS type W-algebras leading to reduced algebras with such infinitely generated classical limit. We also show in examples that the reduced quantum algebras are finitely generated due to quantum corrections arising upon normal ordering the relations obeyed by the classical generators. We apply invariant theory to describe the relations and to argue that classical cosets are infinitely, nonfreely generated in general. As a by-product, we also explain the origin of the previously constructed and so far unexplained deformable quantum W(2,4,6)- and W(2,3,4,5)-algebras.

Original languageEnglish
Pages (from-to)409-445
Number of pages37
JournalNuclear Physics B
Volume420
Issue number1-2
DOIs
Publication statusPublished - May 30 1994

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algebra
brackets
polynomials
rings
generators
projection

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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A class of W-algebras with infinitely generated classical limit. / de Boer, J.; Fehér, L.; Honecker, A.

In: Nuclear Physics B, Vol. 420, No. 1-2, 30.05.1994, p. 409-445.

Research output: Contribution to journalArticle

de Boer, J. ; Fehér, L. ; Honecker, A. / A class of W-algebras with infinitely generated classical limit. In: Nuclear Physics B. 1994 ; Vol. 420, No. 1-2. pp. 409-445.
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