Cohomology of Linear Cycle Sets when the adjoint group is finite abelian

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.

This paper analyzes the second cohomology group [Figure presented], 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.