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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.17798 |
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Table of Contents:
- In this work, we describe local and 2-local $\frac12$-derivations of infinite-dimensional Lie algebras. We prove that all local and 2-local $\frac12$-derivations of the Witt algebra as well as of the positive Witt algebra and the classical one-sided Witt algebra are $\frac12$-derivations. We also give an example of an infinite-dimensional Lie algebra with a local (2-local) $\frac12$-derivation which is not a $\frac12$-derivation. Further we prove that all local (2-local) $\frac12$-derivations on the $\mathcal{W}(a,b)$ algebra are $\frac12$-derivations.