Year: 2026
Type: article
Abstract: Consider A as a unital ∗-algebra. Given elements A,B∈A, the operations A•B=AB+BA* and [A,B]*=AB−BA* represent the skew Jordan product and the skew Lie product, correspondingly. Within this study, we demonstrate that a nonlinear mapping Φ:A→A adhering to Φ[A1•A2•⋯•An−1,An]*=∑j=1n[A1•A2•⋯•Aj−1•Φ(Aj)•Aj+1•⋯•An−1,An]* for every A1,A2,…,An∈A with n≥3, then Φ is an additive ∗-derivation. As an application of our main results, we establish characterizations of prime ∗-algebras, standard operator algebras, von Neumann algebras without central summands of type I1, and factor von Neumann algebras.
Source: Axioms
Authors: Mohammad Shane Alam, Omaima Alshanquiti
Institutions: Aligarh Muslim University, Umm al-Qura University
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
OpenAlex ID: W7129005407