# W-algebras with set of primary fields of dimensions (3, 4, 5) and (3,4,5,6)

Source: [W-algebras with set of primary fields of dimensions (3, 4, 5) and (3,4,5,6)](<https://www.sota2.com/research/paper/68fa240d2c2a37601939ea11>)

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

Data updated: 2025-10-24T07:54:36.707Z

Authors: K. Hornfeck

Published: 1992-12-17T09:45:41.000Z

## Abstract

We show that that the Jacobi-identities for a W-algebra with primary fields of dimensions 3, 4 and 5 allow two different solutions. The first solution can be identified with WA\_4. The second is special in the sense that, even though associative for general value of the central charge, null-fields appear that violate some of the Jacobi-identities, a fact that is usually linked to exceptional W-algebras. In contrast we find for the algebra that has an additional spin 6 field only the solution WA\_5.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/hep-th/9212104>)

[PDF](<https://arxiv.org/pdf/hep-th/9212104.pdf>)