相关论文: Tensor triangular geometry -- Notes for an Oberwol…
These notes are an expanded version of the lectures held in Tromso, in May 2025 at the "Lie-Stormer Summer School : Invariant Theory from classics to modern developments", in the framework of TiME events. We emphasize the analogy between…
We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…
We construct a new class of symmetric algebras of tame representation type that are also the endomorphism algebras of cluster tilting objects in 2-Calabi-Yau triangulated categories, hence all their non-projective indecomposable modules are…
We discuss some basic properties of the graded center of a triangulated category and compute examples arising in representation theory of finite dimensional algebras.
These are the extended notes of a talk I gave at the Geometric Topology Seminar of the Max Planck Institute for Mathematics in Bonn on January 30th, 2012. My goal was to familiarize the topologists with the basics of arithmetic hyperbolic…
In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…
This is an expanded version of the notes by the second author of the lectures on symmetric tensor categories given by the first author at Ohio State University in March 2019 and later at ICRA-2020 in November 2020. We review some aspects of…
We extend work of Balmer, associating filtrations of essentially small tensor triangulated categories to certain dimension functions, to the setting of actions of rigidly-compactly generated tensor triangulated categories on compactly…
For a representation of a finite group $G$ on a complex vector space $V$ we determine when a holomorphic $\binom{p}{q}$-tensor field on the principle stratum of the orbit space $V/G$ can be lifted to a holomorphic $G$-invariant tensor field…
These notes represent the transcript of three, 90 minute lectures given by the second author at the CRM in Barcelona in 2021 as part of the "Higher Structures and Operadic Calculus" workshop. The goal of the series was to introduce and…
We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group $G$, the derived and the stable categories…
We generalize the notion of ends and coends in category theory to the realm of module categories over finite tensor categories. We call this new concept "module (co)end". This tool allows us to give different proofs to several known results…
Triangle presentations are combinatorial structures on finite projective geometries which characterize groups acting simply transitively on the vertices of a locally finite building of type $\tilde{\text{A}}_{n-1}$ ($n\ge3$). From a type…
Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view-spaces of varying dimensions are studied…
These notes are the second part of the tensor calculus documents which started with the previous set of introductory. In the present text, we continue the discussion of selected topics of the subject at a higher level expanding, when…
We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples
We give analogues of the Auslander correspondence for two classes of triangulated categories satisfying certain finiteness conditions. The first class is triangulated categories with additive generators and we consider their endomorphism…
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by…
Support $\tau$-tilting modules correspond to some classes of categorical objects bijectively, such as two-term tilting complexes for any finite dimensional symmetric algebra. This fact motivates us to classify support $\tau$-tilting modules…