Top 20 Operator Algebras Papers: Oct 26 - Nov 1, 2026

We establish a direct connection between the entanglement bootstrap and the Doplicher--Haag--Roberts theory of superselection sectors for two-dimensional quantum spin systems.

We investigate the regularity properties of C*-algebras admitting a weakly selfless unital completely positive map.

We introduce the notion of inner $\mathrm{C}^{\ast}$-selfless groups and study their structural properties.

For actions of discrete amenable groups on unital C*-algebras, we introduce a weak Rokhlin property which leads to a weak tracial approximation of the crossed products by means of finite direct sums of matrix algebras over hereditary subalgebras of the original algebra.

The two separating examples are constructed using relative expansion and twisted spectral-gap techniques, respectively.

In this paper, by replacing ``almost everywhere convergence" with Nelson's convergence in measure, we establish a noncommutative analog of the dominated convergence theorem for $L^\alpha(\mathcal M, \tau)$ under a { significantly weaker dominating condition} than those previously considered.

For a discrete group $G$, we construct an $(n+1)$-dimensional $G$-equivariant Alterfold topological quantum field theory from a $G$-equivariant $S^n$-algebra satisfying strong semisimplicity, complete finiteness, and Morita invariance.

Discretisation with respect to a homological invariant $\mathcal{H}$ holds when $\mathcal{H}(\Omega)$ is an equivalence. We show for example that discretisation with respect to the $K$-theory spectrum $\mathbb{K} \mathfrak{B}_G$ of the permutative category of bisections always holds, establish excision and continuity for this invariant, and use all this and explicit resolutions by independent groupoids to compute it for several families of ample groupoids.

For finite-dimensional quantum channels compatible with a faithful conditional expectation, we show that conditional hyperboundedness and strict GNS contraction together yield a relative entropy contraction.

We introduce quantitative $K$-homology for uniform Roe algebras of discrete proper metric spaces with bounded geometry, based on the controlled $KK$-theory of Willett and Yu.

In this paper, we establish the sharp $2$-logarithmic Sobolev inequality for $q$-Araki-Woods Ornstein-Uhlenbeck semigroups with $-1<q<1$ and obtain hypercontractivity along the Gross curve with the optimal coefficient, and determine the exact hypercontractive time for $1<p\le2\le r<\infty$.

Li proved that the noncommutative tori $A_\theta$ and $A_{g\theta}$ are strongly Morita equivalent whenever $g\in\mathrm{SO}(n,n|\mathbb{Z})$ and $g\theta$ is defined. We study equivariant extensions of these equivalences for canonical finite cyclic group actions.

We prove that, for every countable non-exact discrete group $H$ and every nontrivial countable discrete group $K$, the reduced group $C^*$-algebra $C_r^*(K\wr H)$ is not locally reflexive.

We confirm a conjecture of the first author [SODA'26] on a strong form of pseudo-telepathy for Khot's $d$-to-$1$ games: for every $d\geq 4$, every $\epsilon>0$, and every $k\in\mathbb N$, there is a $d$-to-$1$ label-cover game of classical value less than $\epsilon$ that admits a perfect quantum strategy using finite-dimensional shared entanglement with measurement contexts of radius at least $k$.

In this paper, we determine the complete ground-state spaces for a broad class of generalized stabilizer quantum models defined over CW-decompositions of non-compact manifolds of arbitrary dimensions and topological type.

Building on OpenAI's preprint, we construct, for every real number $r\in(0,1)$, a finitely generated discrete group $G_r$ and a projection $e_r\in C_r^*(G_r)$ whose canonical trace is $r$.

This paper provides a human digestion of a proof of the spectral isometry conjecture for $C^*$-algebras found by GPT-6 Astra.

In this paper, we prove an Adian-Rabin theorem for quantum automorphism groups of graphs, showing that many natural properties of the quantum automorphism group of a graph (including having quantum symmetries) are undecidable.

These notes provide an introduction to Haagerup noncommutative $L^p$ spaces for quantum field theorists.