Related papers: The phantom menace in representation theory

Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…

Ends and end cohomology are powerful invariants for the study of noncompact spaces. We present a self-contained exposition of the topological theory of ends and prove novel extensions including the existence of an exhaustion of a proper…

We identify morphisms of strong profunctors as a categorification of quantum supermaps. These black-box generalisations of diagrams-with-holes are hence placed within the broader field of profunctor optics, as morphisms in the category of…

We deal with several pcf problems; we characterize another version of exponentiation: number of kappa-branches in a tree with lambda nodes, deal with existence of independent sets in stable theories, possible cardinality of ultraproduct,…

We define a finite-dimensional partially formal supermanifold as a manifold having $q$ odd coordinates and $k + l$ even coordinates with $l$ of them taking only nilpotent values. We show that this notion can be used to formulate…

Interpretation problems are eliminated from quantum theory by picturing a quantum history as having been sampled from a probability distribution over the set of histories which are permitted by all relevant boundary conditions. In…

There is a general notion of the magnitude of an enriched category, defined subject to hypotheses. In topological and geometric contexts, magnitude is already known to be closely related to classical invariants such as Euler characteristic…

Let $\Lambda$ be an Artin algebra. In 2014, T. Adachi, O. Iyama and I. Reiten proved that the torsion funtorially finite classes in $\mathrm{mod}\,(\Lambda)$ can be described by the $\tau$-tilting theory. The aim of this paper is to…

We define a dimension for a triangulated category. We prove a representabilityTheorem for a certain class of functors on finite dimensional triangulatedcategories. We study the dimension of the boundedderived category of an algebra or a…

We define a new invariant of finitely generated representations of a finite group, with coefficients in a commutative noetherian ring. This invariant uses group cohomology and takes values in the singularity category of the coefficient…

This text gives a rough, but linear summary covering some key definitions, notations, and propositions from Lambda Calculus: Its Syntax and Semantics, the classical monograph by Barendregt. First, we define a theory of untyped extensional…

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…

This survey is about the fundamentals of the theory of finite dimensional Lie groups over the field of real numbers. The notion of the tangent space of a manifold at a point is considered to be defined via the well known chart and vector…

We will study the resolution dimension of functorially finite subcategories. The subcategories with the resolution dimension zero correspond to ring epimorphisms, and rejective subcategories correspond to surjective ring morphisms. We will…

Let $\Lambda$ be a commutative local uniserial ring of length at least seven with radical factor ring $k$. We consider the category $S(\Lambda)$ of all possible embeddings of submodules of finitely generated $\Lambda$-modules and show that…

In this article I expound an understanding of the quantum mechanics of so-called "indistinguishable" systems in which permutation invariance is taken as a symmetry of a special kind, namely the result of representational redundancy. This…

This work provides an effective algorithm for distinguishing finite quotients between two non-isomorphic finitely generated Fuchsian groups $\Gamma$ and $\Lambda$. It will suffice to take a finite quotient which is abelian, dihedral, a…

Functor morphing provides a method to translate complex representations of automorphism groups of finite modules over finite rings to representations of automorphism groups of functors in some abelian category. In this paper we give an…

We define submersions f between manifolds M and N modelled on locally convex spaces. If the range N is finite-dimensional or a Banach manifold, then these coincide with the naive notion of a submersion. We study pre-images of submanifolds…

This note is a survey on the basic aspects of moduli theory along with some examples. In that respect, one of the purposes of this current document is to understand how the introduction of stacks circumvents the non-representability problem…