arXiv subjects

Cangyuan Wang

Publications and source records attributed to Cangyuan Wang.

3 recordsLinked to original sources

arXiv2026

A note on purely infinite corona algebras and extensions

Let $\mathcal{A}$ be a separable nuclear C*-algebra, and $\mathcal{B}$ be a nonunital separable simple $\mathcal{Z}$-stable C*-algebra. Continuing the work from Gabe-Lin-Ng, we classify all essential extensions, with large complement, of the form $$0 \rightarrow \mathcal{B} \rightarrow \mathcal{E} \rightarrow \mathcal{A} \rightarrow 0,$$ for the following cases: i. $\mathcal{C}(\mathcal{B})$ is properly infinite, and the extension is full. ii. $\mathcal{C}(\mathcal{B})$ is purely infinite (though not necessarily simple). We also have some more general results.

math.OA↗

arXiv2025

A note on proper asymptotic uniqueness for semifinite factors

Let $\mathcal{A}$ be a separable nuclear C*-algebra, and let $\mathcal{M}$ be a semifinite von Neumann factor with separable predual. Let $ϕ, ψ: \mathcal{A} \rightarrow \mathcal{M}$ be essential trivial extensions with $ϕ(a) - ψ(a) \in \mathcal{K}_{\mathcal{M}}$ for all $a \in \mathcal{A}$ such that either both $ϕ$ and $ψ$ (and hence $\mathcal{A}$) are unital or both $ϕ$ and $ψ$ have large complement. Then $ϕ$ and $ψ$ are properly asymptotically unitarily equivalent if and only if $[ϕ, ψ]_{CS} = 0$ in $KK(\mathcal{A}, \mathcal{C}(S \mathcal{K}_{\mathcal{M}}))$.

math.OA↗

arXiv2024

On spectral flow for operator algebras

Spectral flow was first studied by Atiyah and Lusztig, and first appeared in print in the work of Atiyah-Patodi-Singer (APS). For a norm-continuous path of self-adjoint Fredholm operators in the multiplier algebra $\mathcal{M}(\mathcal{B})$ with $\mathcal{B}$ separable and stable, spectral flow roughly measures the ``net mass" of spectrum that passes through zero in the positive direction, as we move along the continuous path. As the index of a Fredholm operator has had many fruitful and important generalizations to general operator algebras, generalizing the spectral flow of a path of self-adjoint Fredholm operators would also be of great interest to operator theory. We develop a notion of spectral flow which works for arbitrary separable stable canonical ideals -- including stably projectionless C*-algebras (which depends on a quite general notion of essential codimension). We show that, under appropriate hypotheses, spectral flow induces a group isomorphism $π_1(Fred_{SA,\infty},pt)\cong K_0(\mathcal{B})$, generalizing a result of APS. We also provide an axiomatization of spectral flow.

math.OA↗