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

We discuss what has been achieved in the past twenty years on the construction and study of a braided finite tensor category structure on a suitable module category for a suitable vertex operator algebra. We identify the main difficult…

This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same $T/I$ class. It is a generalization of the well known \"Ottingen-Riemann torus for triads of…

Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…

This is a survey on spherical Hopf algebras. We give criteria to decide when a Hopf algebra is spherical and collect examples. We discuss tilting modules as a mean to obtain a fusion subcategory of the non-degenerate quotient of the…

These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…

This text is a support for different courses of the master of Mechanics of the University Paris-Saclay. The content of this text is an introduction, for graduate students, to tensor algebra and analysis. Far from being exhaustive, the text…

In a previous paper we constructed rank and support variety theories for "quantum elementary abelian groups," that is, tensor products of copies of Taft algebras. In this paper we use both variety theories to classify the thick tensor…

This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the triangular decomposition of a semisimple…

We compute the tensor triangular spectrum of perfect complexes of filtered modules over a commutative ring, and deduce a classification of the thick tensor ideals. We give two proofs: one by reducing to perfect complexes of graded modules…

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…

Higher-rank Minkowski valuations are efficient means for describing the geometry and connectivity of spatial patterns. We show how to extend the framework of the scalar Minkowski valuations to vector- and tensor-valued measures. The…

These notes grew out of a mini-course given by the second-named author at Casa Matem\'atica Oaxaca in the Fall of 2022. Their purpose is to provide an exposition, directed at graduate students, of the basic properties of complex analytic…

We study tridimensional tensors on the complex field from the point of view of hypermatrices, taking into consideration the problem of determining whether they are degenerate or not, concise or not, what is their essential format if they…

For a given modular tensor category we study representations of the corresponding tube category whose isomorphism classes are modular invariant matrices. In particular, we provide a characterization of these representations in terms of the…

Classifying isomorphism classes of group gradings on algebras presents a compelling challenge, particularly within the realms of non-simple and infinite-dimensional algebras, which have been relatively unexplored. This study focuses on a…

We initiate a study of tensor ideals in linear rigid monoidal categories that are kernels of linear monoidal functors to abelian monoidal categories. We develop general methods and apply them to the category of tilting modules over quantum…

The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning…

Tensor network diagram (graphical notation) is a useful tool that graphically represents multiplications between multiple tensors using nodes and edges. Using the graphical notation, complex multiplications between tensors can be described…

A diagrammatic presentation of functors and natural transformations and the virtues of biadjointness are discussed. We then review a graphical description of the category of Soergel bimodules and a diagrammatic categorification of positive…

Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, Dugger-Shipley, ..., Toen and…