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Item type:Publication, Cleft extensions of weak Hopf algebras(Academic Press Inc., 2020-04-01)In this paper we study the theory of cleft extensions for a weak bialgebra H. Among other results, we determine when two unitary crossed products of an algebra A by H are equivalent and we prove that if H is a weak Hopf algebra, then the categories of H-cleft extensions of an algebra A, and of unitary crossed products of A by H, are equivalent. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Extensions of a family of linear cycle sets(Taylor & Francis, 2026-01-01)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. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, 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.1