PreprintCC0arXiv
Local derivations is a Lie algebra
Abstract
In this paper, we utilize the reflexive hull to unify the concepts of local and almost inner derivations. By investigating the algebraic structure of reflexive hulls, we prove the conjecture on the structure of local derivations proposed by Ayupov, Elduque, and Kudaybergenov (\emph{J. Pure Appl. Algebra}, 2023), as well as the conjecture concerning the structure of almost inner derivations proposed by Burde, Dekimpe, and Verbeke (\emph{J. Algebra Appl.}, 2018).
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BibTeX
@misc{hao2026local,
title = {{Local derivations is a Lie algebra}},
author = {Zeyu Hao and Liangyun Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09198},
eprint = {2609.09198},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09198},
note = {CC0},
}
RIS
TY - UNPB
TI - Local derivations is a Lie algebra
AU - Zeyu Hao
AU - Liangyun Chen
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.09198
UR - https://arxiv.org/abs/2609.09198
AB - In this paper, we utilize the reflexive hull to unify the concepts of local and almost inner derivations. By investigating the algebraic structure of reflexive hulls, we prove the conjecture on the structure of local derivations proposed by Ayupov, Elduque, and Kudaybergenov (\emph{J. Pure Appl. Algebra}, 2023), as well as the conjecture concerning the structure of almost inner derivations proposed by Burde, Dekimpe, and Verbeke (\emph{J. Algebra Appl.}, 2018).
ER -