Introduction. In [14] we began a study of C*-algebras corresponding to projective representations of the discrete Heisenberg group, and classified these C*-algebras up to *-isomorphism. In this sequel to [14] we continue the study of these so-called Heisenberg C*-algebras, first concentrating our study on the strong Morita equivalence classes of these C*-algebras. We recall from [14] that a Hei...

We introduce and study bimeasurings from pairs of bialge-bras to algebras. It is shown that the universal bimeasuring bialgebra construction, which arises from Sweedler's universal measuring coalgebra construction and generalizes the finite dual, gives rise to a contravariant functor on the category of bialgebras adjoint to itself. An interpretation of bimeasurings as algebras in the category o...

We consider the notion of an isomorphism between two hyper BCI-algebras and obtain all of the hyper BCI-algebras of order 3. It is shown that there exist 14 proper hyper BCI-algebras and 5 proper weak hyper BCI-algebras of order 3 up to isomorphism. Finally, further study on the theory of hyper BCI-algebra and its related hyper structure and applications of our results in information sciences a...

Basics of Elliott’s classification program are outlined and juxtaposed with the abstract classification theory from descriptive set theory. Some preliminary estimates on the complexity of the isomorphism relation of separable C*-algebras are given.

The isomorphism problem for group algebras over a field with arbitrary characteristic of some special classes of torsion-free non-abelian groups is explored. Specifically, the following are proved: Suppose F is a field and G is a torsion-free group with centre C(G) such that FG ∼= FH as F -algebras for any group H . Then it is shown that H is torsion-free (provided that FG is without zero divis...

Abstract. We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A1 and A2 are operator algebras, then any bounded epimorphism of A1 onto A2 is completely bounded provided that A2 contains a norming C ∗-subalgebra. We use this result to give some insights into Kadison’s Similarity Problem: we show that every faithful bounded homomo...