Related papers: Higher Morita-Tachikawa correspondence
The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…
In this paper we consider the representation theory of N=1 Super-W-algebras with two generators for conformal dimension of the additional superprimary field between two and six. In the superminimal case our results coincide with the…
In arXiv:1506.05880 we gave a generalization of the theory of quivers with potentials introduced by Derksen-Weyman-Zelevinsky, via completed tensor algebras over $S$-bimodules where $S$ is a finite dimensional basic semisimple algebra. In…
Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories, i.e. the Tomita-Takesaki modular group associated with the von Neumann algebra of a wedge…
We consider a natural generalisation of symmetric Nakayama algebras, namely, symmetric special biserial algebras with at most one non-uniserial indecomposable projective module. We describe the basic algebras explicitly by quiver and…
Gendo-symmetric algebras were introduced by Fang and Koenig as a generalisation of symmetric algebras. Namely, they are endomorphism rings of generators over a symmetric algebra. This article studies various algebraic and homological…
Let $A$ be a finite dimensional algebra over a field $K$ with enveloping algebra $A^e=A^{op} \otimes_K A$. We call algebras $A$ that have the property that the subcategory of Gorenstein projective modules in $mod-A$ coincide with the…
In this paper, we develop two new homological invariants called relative dominant dimension with respect to a module and relative codominant dimension with respect to a module. These are used to establish precise connections between Ringel…
We study the representation theory of finite W-algebras. After introducing parabolic subalgebras to describe the structure of W-algebras, we define the Verma modules and give a conjecture for the Kac determinant. This allows us to find the…
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…
Let k be an algebraically closed field. Given an extension A : B of finite-dimensional k- algebras, we establish criteria ensuring that the representation-theoretic notion of polynomial growth is preserved under ascent and descent. These…
The rigidity degree of a generator-cogenerator determines the dominant dimension of its endomorphism algebra, and is closely related to a recently introduced homological dimension -- rigidity dimension. In this paper, we give explicit…
The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…
W-algebras of finite type are certain finitely generated associative algebras closely related to the universal enveloping algebras of semisimple Lie algebras. In this paper we prove a conjecture of Premet that gives an almost complete…
A noncommutative Kunita-Watanabe-type representation theorem is established for the martingales of quasifree states of CCR algebras. To this end the basic theory of quasifree stochastic integrals is developed using the abstract It\^o…
These notes reflect the contents of three lectures given at the workshop of the 14th International Conference on Representations of Algebras (ICRA XIV), held in August 2010 in Tokyo. We first provide an introduction to quantum loop algebras…
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection…
We give a complete classification of all $d$-representation-finite symmetric Nakayama algebras and of all $d$-representation-finite trivial extensions of path algebras of quivers, over an arbitrary field. As a consequence we get a…
We establish a correspondence between vector-valued modular forms with respect to a symmetric tensor representation and quasimodular forms. This is carried out by first obtaining an explicit isomorphism between the space of vector-valued…
In this paper, we investigate the relative dominant dimension with respect to an injective module and characterize the algebras with finite relative dominant dimension. As an application, we introduce the almost n-precluster tilting module…