5 papers
Cohomology of Trivial Linear Cycle Sets
Jorge Guccione, Juan José Guccione, Christian Valqui
We provide a complete classification of extensions of a trivial linear cycle set H by an abelian group I, under the assumption that both H and I are finite cyclic p-groups with p o…
Cohomology of Linear Cycle Sets when the adjoint group is finite abelian
Jorge Guccione, Juan José Guccione, Christian Valqui
This paper analyzes the second cohomology group of a linear cycle set with coefficients in an abelian group I, for linear cycle sets with commutative adjoint operation, focusing on…
Extensions of a family of Linear Cycle Sets
Jorge Guccione, Juan José Guccione, Christian Valqui
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 c…
Set-theoretic type solutions of the braid equation
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
In this paper we begin the study of set-theoretic type solution of the braid equation. Our theory includes set-theoretical solutions as basic examples. We show that the relationshi…
Hopf q-braces structures on rank one pointed Hopf algebras
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
In this paper we determine all the Hopf q-brace structures on rank one pointed Hopf algebras and compute the socle of each one of them. We also identify which among them are Hopf s…