Lie biderivations on a generalized matrix algebra

Jinhong Zhuang; Yanping Chen; Yijia Tan; Jinhong Zhuang; Yanping Chen; Yijia Tan

doi:10.3934/math.2026336

AIMS Mathematics

2026, Volume 11, Issue 3: 8183-8201. doi: 10.3934/math.2026336

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Research article

Lie biderivations on a generalized matrix algebra

1.
College of Information Engineering, Fujian Business University, Fuzhou 350102, Fujian, China
2.
School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, Fujian, China

Received: 27 January 2026 Revised: 13 March 2026 Accepted: 20 March 2026 Published: 27 March 2026
MSC : 15A78, 16W25, 47B47

In this paper, we investigate the structure of Lie biderivations on a generalized matrix algebra $ \mathcal{G} $. Although results on Lie biderivations are well-established for triangular algebras, the extension to the broader class of generalized matrix algebras has remained largely unexplored, and our work fills this gap. By leveraging the faithful bimodule structure of $ \mathcal{G} $, we prove that, under mild conditions, every Lie biderivation on $ \mathcal{G} $ can be decomposed into the sum of a biderivation and a central mapping. As a direct application, we extend this result to obtain an analogous decomposition for Lie biderivations on full matrix algebras.
- generalized matrix algebra,
- Lie biderivation,
- extremal biderivation,
- biderivation
Citation: Jinhong Zhuang, Yanping Chen, Yijia Tan. Lie biderivations on a generalized matrix algebra[J]. AIMS Mathematics, 2026, 11(3): 8183-8201. doi: 10.3934/math.2026336

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Abstract

In this paper, we investigate the structure of Lie biderivations on a generalized matrix algebra $ \mathcal{G} $. Although results on Lie biderivations are well-established for triangular algebras, the extension to the broader class of generalized matrix algebras has remained largely unexplored, and our work fills this gap. By leveraging the faithful bimodule structure of $ \mathcal{G} $, we prove that, under mild conditions, every Lie biderivation on $ \mathcal{G} $ can be decomposed into the sum of a biderivation and a central mapping. As a direct application, we extend this result to obtain an analogous decomposition for Lie biderivations on full matrix algebras.

References

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