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arXiv · 2501.08357

Extensions of a family of Linear Cycle Sets

Jorge Guccione·Juan José Guccione·Christian Valqui
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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.

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Jorge Guccione, Juan José Guccione, Christian Valqui. 2025-01-14. Extensions of a family of Linear Cycle Sets. https://arxiv.org/abs/2501.08357

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