Local and 2-local $\frac12$-derivations on quasi-filiform Lie algebras of maximum length

Articles in Press

Document Type : Research Paper

Authors

1 Department of Algebra and Functional Analysis, National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan and Department of Mathematics, Tashkent International University of Financial Management and Technologies, Tashkent, Uzbekistan

2 V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

3 V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan and Department of Applied Mathematics and Mathematical Physics, Urgench State University, Urgench, Uzbekistan

10.22034/as.2026.23632.1824

Abstract

We determine all local $\frac12$-derivations of quasi-filiform Lie algebras of maximum length and compute the dimensions of the corresponding spaces. In every case, the space of local $\frac12$-derivations properly contains the space of $\frac12$-derivations. We also construct explicit non-additive 2-local $\frac12$-derivations on each algebra in the classification.

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References

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Algebraic Structures and Their Applications

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Available Online from 07 October 2026

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