A classical result in the theory of Hopf algebras concerns the uniqueness and existence of inte-grals: for an arbitrary Hopf algebra, the integral space has dimension ≤ 1, and for a finite dimensional Hopf algebra, this dimension is exaclty one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode fol...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

Let CK∗ denote the C ∗-algebra defined by the direct sum of all Cuntz-Krieger algebras. We introduce a comultiplication ∆φ and a counit ε on CK∗ such that ∆φ is a nondegenerate ∗-homomorphism from CK∗ to CK∗ ⊗ CK∗ and ε is a ∗-homomorphism from CK∗ to C. From this, CK∗ is a counital non-commutative non-cocommutative C ∗bialgebra. Furthermore, C∗-bialgebra automorphisms, a tensor product of repr...

Let A be a C∗-algebra with a comultiplication ∆. For two states ω and ψ of A which satisfy certain conditions, we construct a unitary R-matrix R(ω, ψ) of the C∗-bialgebra (A,∆) on the tensor product of GNS representations associated with ω and ψ such that the set {R(ω, ψ) : ω, ψ} satisfies the Yang-Baxter equation. Mathematics Subject Classifications (2000). 16W35, 81R50, 46K10.

Background and Aim: The aim of this study was to evaluate the structural integrity of multiple-choice questions according to the Millman checklist, and to assess thedistinguishing power of these questions between weak and strong students in theoretical courses of Periodontics in an academic year (2014-15) in Dental Branch of Tehran Islamic Azad University. Materials and Methods: A total of...