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    Extensions of Linear Cycle Sets and Cohomology
    (Springer Science and Business Media Deutschland GmbH, 2023-03-01)
    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 I (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.
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    Can SUSY Relax Lepton Number Violation Constraints Coming from Loop Corrections to Light Neutrino Masses on the Low-Scale Seesaw Mechanism?
    (American Physical Society, 2023-06-01)
    Heavy neutrinos from the type-I seesaw model can have a large mixing with active states, motivating their search at collider experiments. However, loop corrections to light neutrino masses constrain the heavy neutrinos to appear in pseudo-Dirac pairs, leading to a potential suppression of lepton number violating parameters. In this work we perform a detailed review of a proposal to relax constraints on lepton number violation by adding supersymmetry (SUSY). We define the conditions necessary to maximize the SUSY screening effect, with the objective of allowing a larger mass splitting between low-scale heavy neutrino masses. We find that the sole addition of SUSY does not guarantee a screening, and that favorable cases have some degree of fine-tuning.
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    Cohomology of Linear Cycle Sets when the adjoint group is finite abelian
    (Elsevier, 2026-05-05)
    This paper analyzes the second cohomology group H2 ˛,⤙(H, 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.
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