Generalized derivations and quasi derivations of current $ \text{H} $om-$ \text{L} $ie algebras
Abstract
In this paper, we investigate the structure of generalized derivations and quasiderivations of the tensor product algebra $ \mathcal{H} \otimes \mathcal{A} $, where $ \mathcal{H} $ is a Hom-Lie algebra and $ \mathcal{A} $ is a commutative associative algebra with unity over the field $ \mathcal{K} $. We examine whether every generalized derivation (respectively, quasiderivation) of $ \mathcal{H} \otimes \mathcal{A} $ can be expressed as a sum of a derivation and a linear map in the centroid of $ \mathcal{H} \otimes \mathcal{A} $, provided that this property holds for $ \mathcal{H} $. We establish a partial affirmative result under suitable conditions and discuss the algebraic implications of our findings.
Fields of Study & Subjects
Advanced Topics in Algebra
Homotopy and Cohomology in Algebraic Topology
Advanced Differential Geometry Research
Publication details
- Journal / source
- AIMS Mathematics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 11
- Issue
- 2
- Pages
- 4872–4889
- Publication date
- 1 January 2026