# Classification of Structure Constants for W-algebras from Highest Weights

Source: [Classification of Structure Constants for W-algebras from Highest Weights](<https://www.sota2.com/research/paper/68fa34511e209131ce897d62>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T20:35:27.373Z

Authors: K. Hornfeck

Published: 1993-07-28T10:20:14.000Z

## Abstract

We show that the structure constants of W-algebras can be grouped according to the lowest (bosonic) spin(s) of the algebra. The structure constants in each group are described by a unique formula, depending on a functional parameter h(c) that is characteristic for each algebra. As examples we give the structure constants C\_{33}^4 and C\_{44}^4 for the algebras of type W(2,3,4,...) (that include the WA\_{n-1}-algebras) and the structure constant C\_{44}^4 for the algebras of type W(2,4,...), especially for all the algebras WD\_n, WB(0,n), WB\_n and WC\_n. It also includes the bosonic projection of the super-Virasoro algebra and a yet unexplained algebra of type W(2,4,6) found previously.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/hep-th/9307170>)

[PDF](<https://arxiv.org/pdf/hep-th/9307170.pdf>)