Related papers: A categorical Connes' $\chi(M)$

In this paper we study modular tensor categories (braided rigid balanced tensor categories with additional finiteness and non-degeneracy conditions), in particular, representations of quantum groups at roots of unity. We show that the…

We classify finite pointed braided tensor categories admitting a fiber functor in terms of bilinear forms on symmetric Yetter-Drinfeld modules over abelian groups. We describe the groupoid formed by braided equivalences of such categories…

We discuss the structure of the Motzkin algebra $M_k(D)$ by introducing a sequence of idempotents and the basic construction. We show that $\cup_{k\geq 1}M_k(D)$ admits a factor trace if and only if $D\in \{2\cos(\pi/n)+1|n\geq 3\}\cup…

We first generalize the logarithmic tensor category theory of Huang-Lepowsky-Zhang to the more general case that the module category for a vertex operator algebra $V$ (more generally a M\"{o}bius vertex algebra) might not be closed under…

We show that there is a braided tensor category structure on the category of $C_1$-cofinite modules for the (universal or simple) Virasoro vertex operator algebras of arbitrary central charge. In the generic case of central charge…

We define the notion of a $\lambda$-definable category, a generalisation of the notion of definable category from the model theory of modules. Let ${\cal C}$ be a $\lambda$-accessible additive category. We characterise the additive functors…

In this article, we construct a 2-shaded rigid ${\rm C}^*$ multitensor category with canonical unitary dual functor directly from a standard $\lambda$-lattice. We use the notions of traceless Markov towers and lattices to define the notion…

We show the existence of a finite group $G$ having an irreducible character $\chi$ with Frobenius-Schur indicator $\nu_2(\chi){=}{+}1$ such that $\chi^2$ has an irreducible constituent $\varphi$ with $\nu_2(\varphi){=}{-}1$. This provides…

We show that there is a functor from the category of positive admissible ternary rings to the category of $*$-algebras, which induces an isomorphism of partially ordered sets between the families of $C^*$-norms on the ternary ring and its…

Given a category C acted on by the loop group G((t)), we define its Whittaker model Whit(C) as C^{N((t)),\chi}, where \chi is a non-degenerate character. We study the properties of this construction. When C is the category of sheaves on the…

In our article [arXiv:1511.05226], we studied the commutant $\mathcal{C}'\subset \operatorname{Bim}(R)$ of a unitary fusion category $\mathcal{C}$, where $R$ is a hyperfinite factor of type $\rm II_1$, $\rm II_\infty$, or $\rm III_1$, and…

We calculate Connes' invariant $\chi(M)$ for certain II$_1$ factors $M$ that can be obtained as inductive limits of subfactors with spectral gap, then use this to answer a question he posed in 1975, on the structure of McDuff factors $M$…

We determine the subfactors $N\subset R$ of the hyperfinite $II_1$-factor R with finite index for which the $C^*$-tensor category of the associated $(N,N)$-bimodules is equivalent to the $C^*$-tensor category $\C{U}_G$ of all unitary finite…

We prove that the notion of Drinfeld center defines a functor from the category of indecomposable multi-tensor categories with morphisms given by bimodules to that of braided tensor categories with morphisms given by monoidal bimodules.…

We introduce fusion, contragradient and braiding of Hilbert affine representations of a subfactor planar algebra $P$ (not necessarily having finite depth). We prove that if $N \subset M$ is a subfactor realization of $P$, then the Drinfeld…

To each category C of modules of finite length over a complex simple Lie algebra g, closed under tensoring with finite dimensional modules, we associate and study a category Aff(C)_\kappa of smooth modules (in the sense of Kazhdan and…

A finite bosonic or fermionic symmetry can be described uniquely by a symmetric fusion category $\mathcal{E}$. In this work, we propose that 2+1D topological/SPT orders with a fixed finite symmetry $\mathcal{E}$ are classified, up to $E_8$…

In the paper "Extensional PERs" by P. Freyd, P. Mulry, G. Rosolini and D. Scott, a category $\mathcal{C}$ of "pointed complete extensional PERs" and computable maps is introduced to provide an instance of an \emph{algebraically compact…

We show that every unitarizable fusion category, and more generally every semisimple C*-tensor category, admits a unique unitary structure. Our proof is based on a categorified polar decomposition theorem for monoidal equivalences between…

We show that the core of a weakly group-theoretical braided fusion category $\C$ is equivalent as a braided fusion category to a tensor product $\B \boxtimes \D$, where $\D$ is a pointed weakly anisotropic braided fusion category, and $\B…