Year: 2025
Type: article
Abstract: In this paper, we provide the necessary and sufficient conditions for a Lie centralizer to be proper and a Jordan centralizer to be a centralizer on graded rings. Since every Lie centralizer naturally induces an anti-symmetric mapping and every Jordan centralizer naturally induces a symmetric mapping, our results provide the underlying graded structures reflected in these mappings. As applications, we recover known results for trivial extension algebras and triangular algebras, and additionally characterize Lie (Jordan) centralizers on exterior algebras, whose operations are inherently anti-symmetric.
Source: Symmetry
DOI: 10.3390/sym17101611
Authors: Haoting He, Qikai Wang, Haiyan Zhu
Institution: Zhejiang University of Technology
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Award: G8984849207
OpenAlex ID: W4414590523