相关论文: An Algebraic Duality Theory for Multiplicative Uni…

Let G be a discrete group and $\Gamma$ an almost normal subgroup. The operation of cosets concatanation extended by linearity gives rise to an operator system that is embeddable in a natural C* algebra. The Hecke algebra naturally embeds as…

In [5] the author conjectures and partially shows that the Cuntz semigroup classifies unitary elements of unital AF-algebras. We provide a complete proof by addressing the existence part of the conjecture, under a mild adjustment of both…

A duality theory of bundles of C$^*$-algebras whose fibres are twisted transformation group algebras is established. Classical T-duality is obtained as a special case, where all fibres are commutative tori, i.e. untwisted group algebras for…

We relate commutative algebras in braided tensor categories to braid-reversed tensor equivalences, motivated by vertex algebra representation theory. First, for $\mathcal{C}$ a braided tensor category, we give a detailed construction of the…

We prove the equivalence of two tensor products over a category of W*-algebras with normal (not necessarily unital) *-homomorphisms, defined by Guichardet and Dauns, respectively. This structure differs from the standard tensor product…

The spectral functor of an ergodic action of a compact quantum group G on a unital C*-algebra is quasitensor, in the sense that the tensor product of two spectral subspaces is isometrically contained in the spectral subspace of the tensor…

Let $C$ and $A$ be two unital separable amenable simple C*-algebras with tracial rank no more than one. Suppose that $C$ satisfies the Universal Coefficient Theorem and suppose that $\phi_1, \phi_2: C\to A$ are two unital monomorphisms. We…

C*-endomorphisms arising from superselection structures with non-trivial centre define a 'rank' and a 'first Chern class'. Crossed products by such endomorphisms involve the Cuntz-Pimsner algebra of a vector bundle having the…

In this article we survey some of the recent goings-on in the classification programme of C$^*$-algebras, following the interesting link found between the Cuntz semigroup and the classical Elliott invariant and the fact that the Elliott…

We characterize the simplicity of Pimsner algebras for non-proper C*-correspondences. With the aid of this criterion, we give a systematic strategy to produce outer actions of unitary tensor categories on Kirchberg algebras. In particular,…

We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…

Let $A$ be a $C^*$-algebra, $H$ be a Hilbert $A$-module and $K(H)$ be the closure of the set of finite rank module maps. We show that the $W^*$-algebra of all bounded $A^{**}$-module maps on the smallest self-dual Hilbert $A^{**}$-module…

Given a fusion category $\mathcal{C}$ and an indecomposable $\mathcal{C}$-module category $\mathcal{M}$, the fusion category $\mathcal{C}^*_\mathcal{M}$ of $\mathcal{C}$-module endofunctors of $\mathcal{M}$ is called the (Morita) dual…

We develop an algebraic formalism for topological $\mathbb{T}$-duality. More precisely, we show that topological $\mathbb{T}$-duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known…

Enveloping $C^*$-algebras for some finitely generated $*$-algebras are considered. It is shown that all of the considered algebras are identically defined by their dual spaces. The description in terms of matrix-functions is given. Keywords…

We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of…

Let $\mathcal{H}$ be an infinite dimensional Hilbert space and $\mathcal{B}(\mathcal{H})$ be the C*-algebra of all bounded linear operators on $\mathcal{H}$, equipped with the operator-norm. By improving the Brown-Pearcy construction,…

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways. The first…

We show that there is a functor from the category of positive admissible ternary rings to the category of $*$-algebras, which induces an isomorphism of partially ordered sets between the families of $C^*$-norms on the ternary ring and its…

A surjective endomorphism or, more generally, a polymorphism in the sense of \cite{SV}, of a compact abelian group $H$ induces a transformation of $L^2(H)$. We study the C*-algebra generated by this operator together with the algebra of…