Local and 2-local $\frac{1}2$-derivations of infinite-dimensional Lie algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910146977857536 |
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| author | Ayupov, Shavkat Arislanbay, Abdireymov Yusupov, Bakhtiyor |
| author_facet | Ayupov, Shavkat Arislanbay, Abdireymov Yusupov, Bakhtiyor |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17798 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local and 2-local $\frac{1}2$-derivations of infinite-dimensional Lie algebras Ayupov, Shavkat Arislanbay, Abdireymov Yusupov, Bakhtiyor Rings and Algebras 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. |
| title | Local and 2-local $\frac{1}2$-derivations of infinite-dimensional Lie algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2604.17798 |