We show that every classifiable simple C*-algebra, in particular the Jiang-Su algebra, admits outer actions of several discrete quantum groups, such as finite quantum groups and duals of certain free compact quantum groups. As a consequence of the construction, we provide new examples of hyperfinite subfactors with the Temperley-Lieb-Jones standard invariant and show that $\operatorname{SU}_q(2)$ can act minimally on some Araki-Woods factors for infinitely many $q$.
We study the quantum Cayley graphs associated with the Kac-Paljutkin quantum group. We determine which projections give rise to undirected, irreflexive and connected quantum graphs and classify them up to isomorphism. Their spectra and chromatic numbers are computed. For the special case of the projection $p = I_2$ we...
We show that, for $k\geq 3$, a lattice in the unitriangular Lie group $U_k(\mathbb{R})$ is the fundamental group of a smooth quasi-projective complex algebraic variety if and only if $k=3$. The proof uses the conjugation symmetry and weight conditions of mixed Hodge structure on the Malcev Lie algebra proven by Morgan....
We show that the canonical embeddings of the Jiang--Su algebra $\mathcal Z$ into the universal unital free product $\mathcal Z \ast_{\mathbb C}\mathcal Z$ are not approximately unitarily equivalent. This answers one of the $99$ problems in the list of Schafhauser, Tikuisis, and White. By contrast, we prove that any two...
We prove, under some assumptions, the uniqueness of universal quantum dimension formulae. We first show that the quantum dimensions of classical algebras have a specific form that can be represented universally, in Vogel's sense, as the product/ratio of q-dimension factors with arguments $a\alpha+b\beta+c\gamma$ where...
This paper presents a survey of several classes of Heisenberg-type algebras, including classical, quantum, and generalized variants. We examine the relationships between different families, such as quantum Heisenberg algebras, generalized Heisenberg algebras, quantum generalized Heisenberg algebras, Ore extensions an...
S. A. Lopes, Héctor Suárez, Yésica Suárez· Beiträge zur Algebra und Geo...· 1 citation· ⚡1
A localized quantum unipotent coordinate category C∼w${\tilde{\mathcal{C}}}_{w}$ associated with a Weyl group element w$w$ is a rigid monoidal category that is obtained by applying the localization process to the category Cw${\mathcal{C}}_{w}$ , a subcategory of the category R-gmod$R\text{-}\mathrm{gmod}$ of finite‐dim...
Masaki Kashiwara, Toshiki Nakashima· Proceedings of the London Ma...· 1 citation· ⚡1
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