What question did this study set out to answer?

The aim is to explore the local and 2-local derivations in the class of single diamond thin Lie algebras.

January 26, 2026

Local and 2-local completeness of a class of single diamond thin Lie algebras

Key Points

The aim is to explore the local and 2-local derivations in the class of single diamond thin Lie algebras.
Introduced a class of single diamond thin Lie algebras denoted as 𝒯(Λ).
Utilized properties of index version of Pochhammer and combination symbols.
Determined local and 2-local derivations on 𝒯(Λ).
The codimension of derivations in space of local derivations on 𝒯(Λ) is one.
The codimension in space of 2-local derivations on 𝒯(Λ) is infinite.
𝒯(Λ) is shown to be non-local complete and non-2-local complete.

Abstract

We introduce a class of single diamond thin Lie algebras 𝒯(Λ), where Λ is a sequence of nonzero complex numbers. Using the properties of index version of Pochhammer and combination symbols, we completely determine the local and 2-local derivations on 𝒯(Λ). We show that the codimension of the space of derivations on 𝒯(Λ) in the space of local derivations on 𝒯(Λ) is one, while that in the space of 2-local derivations on 𝒯(Λ) is infinite. These, in particular, imply that 𝒯(Λ) is both non-local complete and non-2-local complete.

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Cite This Study

Xia et al. (Fri,) studied this question.

synapsesocial.com/papers/69770393722626c4468e8933 https://doi.org/https://doi.org/10.1142/s0219498827501477

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