Characterizing Linear Maps Preserving Lie Products and Operator Products
Published:Dec 31, 2025 15:14
•1 min read
•ArXiv
Analysis
This paper investigates the properties of linear maps that preserve specific algebraic structures, namely Lie products (commutators) and operator products (anti-commutators). The core contribution lies in characterizing the general form of these maps under the constraint that the product of the input elements maps to a fixed element. This is relevant to understanding structure-preserving transformations in linear algebra and operator theory, potentially impacting areas like quantum mechanics and operator algebras. The paper's significance lies in providing a complete characterization of these maps, which can be used to understand the behavior of these products under transformations.
Key Takeaways
Reference
“The paper characterizes the general form of bijective linear maps that preserve Lie products and operator products equal to fixed elements.”