9 problems

Let $K$ be a field with a fixed involution, and let $E$ and $F$ be directed graphs. Write $L_K(E)$ and $L_K(F)$ for their Leavitt path algebras, equipped with the induced involutio…

Let ${\mathcal M}$ and ${\mathcal N}$ be type II von Neumann algebras, and let $LS({\mathcal M})$ and $LS({\mathcal N})$ denote their algebras of locally measurable operators. A ri…

Hertweck's blockwise isomorphism conjecture. For every $e\in\operatorname{PCI}({\mathbb Q}G)$,

Let $M$ and $N$ be von Neumann algebras of type II. Let $LS(M)$ and $LS(N)$ denote their algebras of locally measurable operators. A ring isomorphism is a bijective ring homomorphi…

A $C^{*}$-algebra is an algebra over the complex numbers equipped with a compatible involution and complete norm; a map is multiplicative $*$-Lie-type or multiplicative $*$-Jordan-…

Lie triple ring isomorphism conjecture. A mapping $\Phi\colon \operatorname{Alg}\mathcal{N}\longrightarrow \operatorname{Alg}\mathcal{M}$ is a Lie triple ring isomorphism, meaning…

Let $K$ be a field, let $n,d\in\mathbb{N}$, and write $L_K(1,n)$ for the Leavitt algebra of type $(1,n)$. The notation $\operatorname{M}_d(L_K(1,n))$ denotes the ring of…

Let $E$ and $F$ be directed graphs, and let $L_{\mathbb{C}}(E)$ and $L_{\mathbb{C}}(F)$ be their Leavitt path algebras over the complex numbers, while $C^*(E)$ and $C^*(F)$ are the…

Let $E$ and $F$ be directed graphs, and let $L_{\a0\mathbb{C}}(E)$ and $L_{\a0\mathbb{C}}(F)$ denote their Leavitt path algebras over the complex numbers, with the complex-conjugat…