On the Centre of Crossed Modules of Lie Algebras | Synapse
March 28, 2026
On the Centre of Crossed Modules of Lie Algebras
Key Points
The aim is to explore the relationship between crossed modules of Lie algebras and their centres.
Studied the structure of crossed modules of Lie algebras
Analyzed homotopy properties
Examined definitions and relationships in algebraic structures
Confirmed that the homotopy of the centre relates closely to the structure of crossed modules
Identified key properties of the algebraic structures involved
Abstract
This paper studies the relationship between crossed modules of Lie algebras and their centres. We show that the homotopy of the centre of any crossed module