相关论文: Meromorphic tensor categories

In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…

We present explicit examples finite tensor categories that are C_2-graded extensions of the corepresentation category of certain finite-dimensional non-semisimple Hopf algebras.

We construct tensor and bitensor categories with given Grothedieck rig (fusion algebra) in simple cases. The results provide examples on which to test the conjectural construction of 4-D TQFT's proposed by Crane and Frenkel and shed light…

Category theoretic aspects of non-rational conformal field theories are discussed. We consider the case that the category C of chiral sectors is a finite tensor category, i.e. a rigid monoidal category whose class of objects has certain…

We find general relations between RG equations and planar unitarity-analyticity. These relations are summarized in meromorphization procedure, generalizing the Pad\'e approximation in the limit of infinite order. We also investigate…

We review briefly the existing vertex-operator-algebraic constructions of various tensor category structures on module categories for affine Lie algebras. We discuss the results first conjectured in the work of Moore and Seiberg that led us…

Let $(\mathcal{C}, \otimes)$ be a monoidal dg-category. We construct a complex controlling the deformation of the monoidal structure on $\mathcal{C}$ together with the deformation of the underlying dg-category itself. We show that in the…

We define integrable representations of quantum toroidal algebras of type A by tensor product, using the Drinfeld "coproduct". This allow us to recover the vector representations recently introduced by Feigin-Jimbo-Miwa-Mukhin [6] and…

This is the second part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part II), we develop logarithmic formal…

This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…

We review some recent advances in modular representation theory of symmetric groups and related Hecke algebras. We discuss connections with Khovanov-Lauda-Rouquier algebras and gradings on the blocks of the group algebras $F\Sigma_n$, which…

We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of bounded operators. We examine classes of functors and natural transformations with good measure theoretic properties, providing in the end a…

We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…

Following an idea of Nigel Higson, we develop a method for proving the existence of a meromor-phic continuation for some spectral zeta functions. The method is based on algebras of generalized differential operators. The main theorem…

This article contains a review of categorifications of semisimple representations of various rings via abelian categories and exact endofunctors on them. A simple definition of an abelian categorification is presented and illustrated with…

We construct categorifications of tensor products of arbitrary finite-dimensional irreducible representations of $\mathfrak{sl}_k$ with subquotient categories of the BGG category $\mathcal{O}$, generalizing previous work of Sussan and…

We construct recursion categories from categories of coalgebras. Let $F$ be a nontrivial endofunctor on the category of sets that weakly preserves pullbacks and such that the category $\textbf{Set}_F$ of $F$-coalgebras is complete. The…

Fusion categories are fundamental objects in quantum algebra, but their definition is narrow in some respects. By definition a fusion category must be k-linear for some field k, and every simple object V is strongly simple, meaning that (V)…

We develop the notion of deformations using a valuation ring as ring of coefficients. This permits to consider in particular the classical Gerstenhaber deformations of associative or Lie algebras as infinitesimal deformations and to solve…

This is the eighth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part VIII), we construct the braided…