MathOverflow

Let $M$ be a Type III₁ factor with separable predual, and let $\omega_B, \omega_{B'}$ be faithful normal states, with modular groups $\sigma^B, \sigma^{B'}$. Call a normal state $\omega$ flow-$C^k$ for $\omega_B$ if $t\mapsto\omega\circ\sigma^B_t$ is...

I have an action of a group G of order 16 on $\mathbb Z/5$. The group has two generators $a, b$, of order 2 and 4 respectively, and they act on a generator $x$ of $\mathbb Z/5$ as $a(x) = 4x$ and $b(x) = 2x$. Since #G is coprime to 5, the $\overline...

Here is the context. Let $\mathcal{O}$ be a $\infty$-operad and $q:\mathcal{C}^\otimes\rightarrow\mathcal{O}^\otimes$ a map of $\infty$-operads exhibiting $\mathcal{C}=\mathcal{C}^\otimes\times_{\mathcal{O}^\otimes}\mathcal{O}$ as a $\mathcal{O}$-monoidal...

Let $f: \mathbb{N} \to \mathbb{T}$ be a completely multiplicative function, and let $(X_f, \mu, T)$ be the associated topological dynamical system, where $X_f \subseteq \mathbb{T}^{\mathbb{N}}$ is the orbit closure of $(f(n))_{n \geq 1}$ under the left...