Related papers: Quantity vs. size in representation theory
For a finite-dimensional algebra {\Lambda}, we establish an explicit bijection between widely generated torsion(-free) classes and semibricks in mod {\Lambda}. Using the kappa order on the lattice of torsion classes with canonical join…
A torsion class $\mathcal{T}$ of the module category $\operatorname{\mathsf{mod}} A$ of a finite dimensional algebra $A$ over a field $K$ is said to be compact if there exists a module $M \in \operatorname{\mathsf{mod}} A$ such that…
Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…
The dimension of any module over an algebra of affiliated operators ${\mathcal U}$ of a finite von Neumann algebra ${\mathcal A}$ is defined using a trace on ${\mathcal A}.$ All zero-dimensional ${\mathcal U}$-modules constitute the torsion…
We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…
Categories of models of algebraic theories have good categorical properties except for gluing. Building upon insights and examples from Synthetic Differential Geometry, we introduce a generalisation of models of algebraic theories to…
Let H be a finite-dimensional quasibialgebra. We show that H is a quasi-Hopf algebra if and only if the category of its finite-dimensional left modules is rigid if and only if a structure theorem for Hopf modules over H holds. We also show…
In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…
From the viewpoint of higher dimensional Auslander-Reiten theory, we introduce a new class of finite dimensional algebras of global dimension n, which we call n-representation infinite. They are a certain analog of representation infinite…
Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit…
It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…
Given a hyper loop algebra over a non-algebraically closed field, we address multiplicity problems in the underlying abelian tensor category of finite-dimensional representations. Namely, we give formulas for the l-characters of the simple…
We construct from a finitary exact category with duality a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of the category. We study in detail Hall modules arising from the…
Let $H$ be a hereditary artin algebra of finite representation type. We first determine all hammocks in the Auslander-Reiten quiver $\GaH$ of $\mmod H$, the category of finitely generated left $H$-modules. This enables us to obtain an…
In recent years, researchers have discovered various large algebraic structures that have surprising finiteness properties, such as FI-modules and Delta-modules. In this paper, we add another example to the growing list: we show that…
In this paper we continue the study of representation theory of formal distribution Lie superalgebras initiated in q-alg/9706030. We study finite Verma-type conformal modules over the N=2, N=3 and the two N=4 superconformal algebras and…
Let L be a finite-dimensional Lie algebra over a field of non-zero characteristic. By a theorem of Jacobson, L has a finite-dimensional faithful module which is completely reducible. We show that if the field is not algebraically closed,…
Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of…
A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions of quantum groups, and proofs of the…
A representation embedding between cartesian theories can be defined to be a functor between respective categories of models that preserves finitely-generated projective models and that preserves and reflects certain epimorphisms. This…