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General properties of classical W algebras

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F. Delduc, L. Frappat, E. Ragoucy, P. Sorba

High Energy Physics - Theory · Submitted 6 Dec 1993

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Factorizing out this spin 1 subalgebra gives rise to a new $W$ structure which we interpret either as a rational finitely generated $W$ algebra, or as a polynomial non linear $W_\infty$ realization.

how it is stated · asserted 0.93 read the record →

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arXiv IDhep-th/9312041 (version 1)
Pith ID32QOJU4H, Pith's permanent record of this paper and its review
CitationE. Ragoucy, F. Delduc, L. Frappat, P. Sorba. "General properties of classical W algebras." arXiv:hep-th/9312041 (1993). https://pith.science/paper/32QOJU4H
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,152 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.12 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

After some definitions, we review in the first part of this talk the construction and classification of classical $W$ (super)algebras symmetries of Toda theories. The second part deals with more recently obtained properties. At first, we show that chains of $W$ algebras can be obtained by imposing constraints on some $W$ generators: we call secondary reduction such a gauge procedure on $W$ algebras. Then we emphasize the role of the Kac-Moody part, when it exists, in a $W$ (super) algebra. Factorizing out this spin 1 subalgebra gives rise to a new $W$ structure which we interpret either as a rational finitely generated $W$ algebra, or as a polynomial non linear $W_\infty$ realization. (Plenary talk presented by P. SORBA at the $XXII^{th}$ International Conference on Differential Geometric Methods in Theoretical Physics. Ixtapa Mexico, September 1993.)

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 After some definitions, we review in the first part of this talk the construction and classification of classical $W$ (super)algebras symmetries of Toda theories. background 0.78 0.39 0.04 asserted 0.75
s1 The second part deals with more recently obtained properties. contribution 0.51 0.24 0.03 asserted 0.70
s2 At first, we show that chains of $W$ algebras can be obtained by imposing constraints on some $W$ generators: we call secondary reduction such a gauge procedure on $W$ algebras. method 0.56 0.83 0.13 asserted 1.00
s3 Then we emphasize the role of the Kac-Moody part, when it exists, in a $W$ (super) algebra. contribution 0.73 0.46 0.06 asserted 0.96
s4 Factorizing out this spin 1 subalgebra gives rise to a new $W$ structure which we interpret either as a rational finitely generated $W$ algebra, or as a polynomial non linear $W_\infty$ realization. interpretation 0.87 0.77 0.27 asserted 0.93
s5 (Plenary talk presented by P. background 0.99 0.07 0.01 unclear 0.92
s6 SORBA at the $XXII^{th}$ International Conference on Differential Geometric Methods in Theoretical Physics. background 0.99 0.04 0.01 unclear 0.89
s7 Ixtapa Mexico, September 1993.) background 0.99 0.03 0.01 unclear 0.96

What kind of paper the classifier reports this is: review 0.81 · evidence from proof or derivation 0.83.

What was examined, and what was not

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  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

After some definitions, we review in the first part of this talk the construction and classification of classical $W$ (super)algebras symmetries of Toda theories. The second part deals with more recently obtained properties. At first, we show that chains of $W$ algebras can be obtained by imposing constraints on some $W$ generators: we call secondary reduction such a gauge procedure on $W$ algebras. Then we emphasize the role of the Kac-Moody part, when it exists, in a $W$ (super) algebra. Factorizing out this spin 1 subalgebra gives rise to a new $W$ structure which we interpret either as a rational finitely generated $W$ algebra, or as a polynomial non linear $W_\infty$ realization. (Plenary talk presented by P. SORBA at the $XXII^{th}$ International Conference on Differential Geometric Methods in Theoretical Physics. Ixtapa Mexico, September 1993.)

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States the same result 1 paper
  • Factoring out the spin $1$ subalgebra of a $ W $ algebra leads to a new $ W $ structure which can be seen either as a rational finitely generated $ W $ algebra or as a polynomial non-linear $ W_\infty$ realization.

    Rational $ W $ algebras from composite operators · 1.00

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