Related papers: Almost laura algebras
We describe the structure of semi-regular Auslander-Reiten components of artin algebras without external short paths in the module category. As an application we give a complete description of self-injective artin algebras whose…
In this paper we define almost gentle algebras. They are monomial special multiserial algebras generalizing gentle algebras. We show that the trivial extension of an almost gentle algebra by its minimal injective co-generator is a symmetric…
This paper introduces and investigates the structure of $\delta$-Leibniz algebras, which serve as a parametric generalization of classical Leibniz algebras defined by a scalar $\delta$. The authors define $\delta$-Lie algebras, $\delta$-Lie…
We extend the classical notion of standardly stratified $k$-algebra (stated for finite dimensional $k$-algebras) to the more general class of rings, possibly without $1,$ with enough idempotents. We show that many of the fundamental…
In this paper we show that how the representation theory of subcategories (of the category of modules over an Artin algebra) can be connected to the representation theory of all modules over some algebra. The subcategories dealing with are…
Given an arbitrary algebra $A$ we may associate to it a special endomorphism algebra, $R_A$, introduced by Auslander. Dlab and Ringel constructed a heredity chain for $R_A$, proving that every algebra $A$ has an associated highest weight…
In this paper, we define on one hand, the notions of characteristics as well as central characteristics ideals of a given Leibniz algebra g and provide a necessary condition under which for two given subalgebras J and K of g such that, J IS…
We consider the problem of classifying gradings by groups on a finite-dimensional algebra $A$ (with any number of multilinear operations) over an algebraically closed field. We introduce a class of gradings, which we call almost fine, such…
A new class of completely integrable models is constructed. These models are deformations of the famous integrable and exactly solvable Gaudin models. In contrast with the latter, they are quasi-exactly solvable, i.e. admit the algebraic…
We introduce tabular algebras, which are simultaneous generalizations of cellular algebras (in the sense of Graham-Lehrer) and table algebras (in the sense of Arad-Blau). We show that if a tabular algebra is equipped with a certain kind of…
We introduce the notion of a cellular system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for an algebra to be quasi-hereditary is the existence of a full divisible cellular…
The notion of almost elementariness for a locally compact Hausdorff \'{e}tale groupoid $\mathcal{G}$ with a compact unit space was introduced by the authors as a sufficient condition ensuring the reduced groupoid $C^*$-algebra…
In this paper we introduce a special kind of relative (co)resolutions associated to a pair of classes of objects in an abelian category $\mathcal{C}.$ We will see that, by studying these relative (co)resolutions, we get a possible…
Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as…
Classical affine Lie algebras appear e.g. as symmetries of infinite dimensional integrable systems and are related to certain differential equations. They are central extensions of current algebras associated to finite-dimensional Lie…
We introduce the notions of quasi-Laurent and Laurent families of simple modules over quiver Hecke algebras of arbitrary symmetrizable types. We prove that such a family plays a similar role of a cluster in the quantum cluster algebra…
In this paper, we introduce the concept of a (lattice) skew Hilbert algebra as a natural generalization of Hilbert algebras. This notion allows a unified treatment of several structures of prominent importance for mathematical logic, e.g.…
We introduce a new family of superalgebras which should be considered as a super version of the Khovanov-Lauda-Rouquier algebras. Let $I$ be the set of vertices of a Dynkin diagram with parity. To this data, we associate a family of graded…
The categories of almost modules and almost algebras are introduced as a convenient setting for the development of Faltings' method of almost etale extensions. After some preliminaries of general "almost homological algebra" we construct…
This article consists of an introduction to Iyama's higher Auslander-Reiten theory for Artin algebras from the viewpoint of higher homological algebra. We provide alternative proofs of the basic results in higher Auslander-Reiten theory,…