Extensions of a family of linear cycle sets

Guccione J.A.; Guccione J.J.; Valqui C. · Communications in Algebra (2026) · DOI: 10.1080/00927872.2025.2569477

Resumen

This paper explores the cohomology of linear cycle sets, focusing on extensions of a specific linear cycle set H by an abelian group I. We derive explicit formulas for the second cohomology group, which classifies these extensions, and establish conditions under which the extensions are fully determined. Key results include a characterization of extensions when I lies in the socle of the extended structure and H is trivial, and the construction of explicit examples for both trivial and non-trivial cases. The paper provides a systematic approach to understanding the structure of these extensions, with applications to various families of abelian groups.

Instituciones: Pontificia Universidad Católica del Perú