Crystal and Molecular Structure of (BzlMe3N) 2 + [Fe2OCl6]2-

The crystal and molecular structure of (BzlMe₃N) ₂ ⁺ [Fe₂OCl₆]^2- has been determined. The asymmetric unit contains two benzyltrimethylammonium cations and two half -oxo-bis(trichloro-iron(III)) anions. The bridging -oxygen atoms of these anions are located over crystallographic symmetry elements. Therefore, the two anions resulting from the symmetry operations correspond to two different conformers presenting angular and linear dispositions of the Fe-O-Fe bond angle. Mössbauer spectrum consists of two asymmetric lines that are adequately simulated by two equally populated quadrupole doublets associated with the two iron sites.     

Yetter–Drinfeld Modules over Weak Braided Hopf Monoids and Center Categories

In this paper,we introduce several centralizer constructions in a monoidal context and establish a monoidal equivalence with the category of Yetter–Drinfeld modules over a weak braided Hopf monoid.We apply the general result to the calculus of the center in module categories.     

Crossed Products over Weak Hopf Algebras Related to Cleft Extensions and Cohomology

The authors present the general theory of cleft extensions for a cocommutative weak Hopf algebra H.For a right H-comodule algebra,they obtain a bijective correspondence between the isomorphisms classes of H-cleft extensions AH → A,where AH is the subalgebra of coinvariants,and the equivalence classes of crossed systems for H over AH.Finally,they establish a bijection between the set of equivalence classes of crossed systems with a fixed weak H-module algebra structure and the second cohomology group HφZ(AH)2(H,Z(AH)),where Z(AH)is the center of AH.