English

Extensions of Linear Cycle Sets

K-Theory and Homology 2021-11-16 v1

Abstract

We generalize the cohomology theory for linear cycle sets introduced by Lebed and Vendramin. Our cohomology classifies extensions of linear cycle sets by trivial ideals, whereas the cohomology of Lebed and Vendramin only deals with central ideals II (which are automatically trivial). Therefore our theory gives an analog to the theory of extensions of braces by trivial ideals constructed by Bachiller, but from a cohomological point of view. We also study the general notions of extensions of linear cycle sets and the equivalence of extensions.

Keywords

Cite

@article{arxiv.2111.07953,
  title  = {Extensions of Linear Cycle Sets},
  author = {Jorge A. Guccione and Juan J. Guccione and Christian Valqui},
  journal= {arXiv preprint arXiv:2111.07953},
  year   = {2021}
}

Comments

15 pages

R2 v1 2026-06-24T07:39:17.936Z