Extensions of a family of Linear Cycle Sets
Group Theory
2025-01-16 v1 K-Theory and Homology
Abstract
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.
Cite
@article{arxiv.2501.08357,
title = {Extensions of a family of Linear Cycle Sets},
author = {Jorge Guccione and Juan José Guccione and Christian Valqui},
journal= {arXiv preprint arXiv:2501.08357},
year = {2025}
}