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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 ...

We compare the restriction to the context of weak Hopf algebras of the notion of crossed product with a Hopf algebroid introduced in [Cleft extensions of Hopf algebroids, Appl. Categor. Struct.14(5–6) (2006) 431–469] with ...

This thesis investigates the properties of weak bialgebras and weak Hopf algebras, their (co)representations, and applications in groupoids, path algebras, and Lie algebroids. The research employs algebraic and categorical ...

Given any simple biorientable graph it is shown that there exists a weak *-Hopf algebra constructed on the vector space of graded endomorphisms of essential paths on the graph. This construction is based on a direct sum ...

In this work, we study the notion of differential calculus associated to an associative algebra, from its origin in manifolds geometry, to some generalizations in non commutative differential geometry. In particular, we ...