相关论文: Tensor triangular geometry -- Notes for an Oberwol…

Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…

The aim of this note is to give a gentle introduction to algebras of partial triangulations of marked surfaces, following the structure of a talk given during the 49th symposium on ring theory and representation theory, held in Osaka. This…

These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.

We give a review of some recent developments in the theory of tensor categories. The topics include realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory,…

This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…

We introduce and study a category of algebras strongly connected with the structure of the Gelfand-Tsetlin subalgebras of the endomorphism algebras of Bott-Samelson bimodules. We develop a series of techniques that allow us to obtain…

In the paper `On the Dirac-Frenkel Variational Principle on Tensor Banach Spaces', we provided a geometrical description of manifolds of tensors in Tucker format with fixed multilinear (or Tucker) rank in tensor Banach spaces, that allowed…

The main goal of this paper is to study the geometric structures associated with the representation of tensors in subspace based formats. To do this we use a property of the so-called minimal subspaces which allows us to describe the tensor…

Given a finite modular tensor category, we associate with each compact surface with boundary a cochain complex in such a way that the mapping class group of the surface acts projectively on its cohomology groups. In degree zero, this action…

We study tensor categories that interpolate the representation categories of finite classical groups. There are (at least) two ways to approach these categories: via ultraproducts and via oligomorphic groups. Both have strengths and…

Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…

We develop a theory of cosupport and costratification in tensor triangular geometry. We study the geometric relationship between support and cosupport, provide a conceptual foundation for cosupport as categorically dual to support, and…

We study Tate motives with integral coefficients through the lens of tensor triangular geometry. For some base fields, including the field of algebraic numbers and the algebraic closure of a finite field, we arrive at a complete description…

We study tensor network varieties associated with the triangular graph, with a focus on the case where one of the physical dimensions is 2. This allows us to interpret the tensors as pencils of matrices. We provide a complete…

For any essentially small triangulated category the centre of its lattice of thick subcategories is introduced; it is a spatial frame and yields a notion of central support. A relative version of this centre recovers the support theory for…

We provide an axiomatic approach for studying support varieties of objects in a triangulated category via the action of a tensor triangulated category, where the tensor product is not necessarily symmetric. This is illustrated by examples,…

Using M-theory in physics, Cho, Gang, and Kim (JHEP 2020, 115 (2020) ) recently outlined a program that connects two parallel subjects of three dimensional manifolds, namely, geometric topology and quantum topology. They suggest that…

We introduce the notion of meromorphic tensor category and illustrate it in several examples. They include representations of quantum affine algebras, chiral algebras of Beilinson and Drinfeld, G-vertex algebras of Borcherds, and…

The purpose of this paper is to give an explicit description of the trivial and alternating components of the irreducible representation decomposition of the bigraded module obtained as the tensor square of the coinvariant space for…

We study the uniqueness of enhancements of tensor-triangulated categories. To do so, we provide conditions under which these enhancements interact well with categorical decompositions. As an application we obtain new results about the…