No abstract

In this paper, we present three limit representations of the core-EP inverse.The first approach is based on the full-rank decomposition of a given matrix.The second and third approaches, which depend on the explicit expression of the core-EP inverse, are established. The corresponding limit representations of the dual core-EP inverse are also given. In particular, limit representations of the core and dual core inverse are derived.

We discuss properties of Yetter-Drinfeld modules over weak bialgebras over commutative rings. The categories of left-left, left-right, right-left and right-right Yetter-Drinfeld modules over a weak Hopf algebra are isomorphic as braided monoidal categories. Yetter-Drinfeld modules can be viewed as weak Doi-Hopf modules, and, a fortiori, as weak entwined modules. If H is finitely generated and projective, then we introduce the Drinfeld double using duality results between entwining structures and smash product structures, and show that the category of Yetter-Drinfeld modules is isomorphic to the category of modules over the Drinfeld double. The category of finitely generated projective Yetter-Drinfeld modules over a weak Hopf algebra has duality.1991 Mathematics Subject Classification. 16W30. Research supported by the projects G.0278.01 "Construction and applications of noncommutative geometry: from algebra to physics" from FWO-Vlaanderen and "New computational, geometric and algebraic methods applied to quantum groups and differential operators" from the Flemish and Chinese governments.

No abstract

No abstract