We show that every groupoid C*-algebra is isomorphic to its opposite, and deduce there exist C*-algebras are not stably C*-algebras, though many of them twisted C*-algebras. also prove the opposite algebra a section Fell bundle over natural bundle.

we investigate the problem of the existence of a frame forright ideals of a C*-algebra A, without the use of the Kasparov stabilizationtheorem. We show that this property can not characterize A as a C*-algebraof compact operators.

It is shown that every  almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...

Orders in indefinite quaternion algebras provide Fuchsian groups acting on the Poincare half-plane, used to construct the associated Shimura curves. We explain how, by using embedding theory, the elements of those Fuchsian groups depend on representations of integers by suitable ternary quadratic forms. Thus the explicit computation of those representations leads to explicit presentations and f...

We prove that two unital dual operator algebras A,B are stably isomorphic if and only if they are ∆-equivalent [7], if and only if they have completely isometric normal representations α, β on Hilbert spaces H,K respectively and there exists a ternary ring of operators M ⊂ B(H,K) such that α(A) = [M∗β(B)M]−w and β(B) = [Mα(A)M∗]−w .

In this work we study a new equivalence relation between w∗ closed algebras of operators on Hilbert spaces. The algebras A and B are called TRO equivalent if there exists a ternary ring of operatorsM (i.e. MM∗M ⊂ M) such that A = [M∗BM]−w ∗ and B = [MAM∗]−w ∗ . We prove that two reflexive algebras are TRO equivalent if and only if there exists a ∗ isomorphism between the commutants of their dia...

We consider the class of algebras of rank 4 equipped with a standard involution over an arbitrary base ring. In particular, we characterize quaternion rings, those algebras defined by the construction of the even Clifford algebra. A quaternion algebra is a central simple algebra of dimension 4 over a field F . Generalizations of the notion of quaternion algebra to other commutative base rings R...

We generalize the main theorem of Rieffel for Morita equivalence of W -algebras to the case of unital dual operator algebras: two unital dual operator algebras A,B have completely isometric normal representations α, β such that α(A) = [Mβ(B)M] ∗ and β(B) = [Mα(A)M] ∗ for a ternary ring of operators M (i.e. a linear space M such that MMM ⊂ M) if and only if there exists an equivalence functor F ...