Cohomology of linear cycle sets when the adjoint group is finite abelian
Abstract
This paper analyzes the second cohomology group of a linear cycle set with coefficients in an abelian group I, for linear cycle sets with commutative adjoint operation, focusing on the finite abelian case. It aims to classify extensions of such structures through cohomological methods. Techniques are developed to systematically construct explicitly 2-cocycles. Finally, some illustrative examples are explored to validate the theoretical framework.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Advanced Topics in Algebra
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Journal of Algebra
- Volume
- 702
- Pages
- 265–301
- Publication date
- 5 May 2026
- Language
- EN