In this paper, we try to attack a conjecture of Araujo and Jarosz that every bijective linear map θ between C*-algebras, with both θ and its inverse θ−1 preserving zero products, arises from an algebra isomorphism followed by a central multiplier. We show it is true for CCR C*-algebras with Hausdorff spectrum, and in general, some special C*-algebras associated to continuous fields of C*-algebras.

Exploiting the graph product structure and results concerning amalgamated free products of C⁎-algebras we provide an explicit computation K-theoretic invariants right-angled Hecke C⁎-algebras, including concrete algebraic representants a basis in K-theory. On way, show that these algebras are KK-equivalent with their undeformed counterparts satisfy UCT. Our applied to study isomorphism problem ...

Abstract We consider two inclusions of $C^{*}$ -algebras whose small have approximate units the large and their spaces all bounded bimodule linear maps. suppose that are strongly Morita equivalent. In this paper, we shall show there exists an isometric isomorphism from one maps to other space study basic properties about isomorphism. And, using isomorphism, define Picard group for a map discuss...

Let hom-Ln(C) be the algebraic set of complex n-dimensional hom-Lie algebras. The group GL(n,C) acts on it via change basis. We classify structures with nilpotent twisting map 3-dimensional Lie algebras, up to isomorphism, and we give classification orbit closures in such family. For this purpose, introduce some invariants algebras study both problems. ideas techniques presented here can easily...

We prove that the isomorphism relation for separable C∗-algebras, and also the relations of complete and n-isometry for operator spaces and systems, are Borel reducible to the orbit equivalence relation of a Polish group action on a standard Borel space.

We show that the isomorphism relation for countable Boolean algebras is Borel complete, i.e., the isomorphism relation for arbitrary countable structures is Borel reducible to that for countable Boolean algebras. This implies that Ketonen’s classification of countable Boolean algebras is optimal in the sense that the kind of objects used for the complete invariants cannot be improved in an esse...

In the present note, which is second part of a work concerning study set symmetric states, we introduce extension Klein transformation for general Fermi tensor product two $\bz^2$ graded $C^*$-algebras, under condition that grading one involved algebras inner. After extending construction to $C^*$-inductive limits, such realises canonical $*$-isomorphism between $\bz^2$-graded $C^*$-algebras ma...