Related papers: Indecomposables live in all smaller lengths

We give a characterisation of representation-finite symmetric algebras of period four, and describe their basic algebras. In particular, if such an algebra is indecomposable, it has at most two simple modules.

Recollements of derived module categories are investigated, using a new technique, ladders of recollements, which are mutation sequences. The position in the ladder is shown to control whether a recollement restricts from unbounded to…

The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.

The paper explores the indecomposable submodule structures of quantum divided power algebra $\mathcal{A}_q(n)$ defined in \cite{HU} and its truncated objects $\mathcal{A}_q(n, \bold m)$. An "intertwinedly-lifting" method is established to…

We construct new families of U_q(gl_n)-modules by continuation from finite dimensional representations. Each such module is associated with a combinatorial object - admissible set of relations defined in \cite{FRZ}. More precisely, we prove…

We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number of (isoclasses of) these modules.

Let $(\mathfrak{g},[p])$ be a finite dimensional restricted Lie algebra over a perfect field $\mathbbm{k}$ of characteristic $p\!\ge \!3$. By combining methods from recent work of Benson-Carlson \cite{BC20} with those of \cite{CF21,Fa17} we…

Given a skeletally small category $\mathcal{C}$, we show that any locally finite endo-length $\mathcal{C}$-module is the direct sum of indecomposable $\mathcal{C}$-modules, whose endomorphism algebra is local.

We prove that among the finite dimensional algebras of finite representation type those that are string algebras are precisely the ones that have the property that the middle term of an arbitrary extension of indecomposable modules has at…

Let A be a finite-dimensional algebra. If A is self-injective, then all modules are reflexive. Marczinzik recently has asked whether A has to be self-injective in case all the simple modules are reflexive. Here, we exhibit an 8-dimensional…

We construct all solvable Lie algebras with a specific n-dimensional nilradical n_{n,3} which contains the previously studied filiform nilpotent algebra n_{n-2,1} as a subalgebra but not as an ideal. Rather surprisingly it turns out that…

We introduce the $N=2$ Lie conformal superalgebras ${\frak {K}}(p)$ of Block type, and classify their finite irreducible conformal modules for any nonzero parameter $p$. where $p$ is a nonzero complex number. In particular, we show that…

Based on previous results on the classification of finite-dimensional Nichols algebras over dihedral groups and the characterization of simple modules of Drinfeld doubles, we compute the irreducible characters of the Drinfeld doubles of…

It is shown that the gentle one-cycle algebra $\Lambda(n-1,1,1)$ has Hall polynomials. The Hall polynomials are explicitly given for all triples of indecomposable modules, and as a consequence, the Ringel--Hall Lie algebra of…

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,…

Let $Q$ be the 3-Kronecker quiver, i.e., $Q$ has two vertices, labeled by 1 and 2, and three arrows from 2 to 1. Fix an algebraically closed field $k$. Let $\mathcal{C}$ be a regular component of the Auslander-Reiten quiver containing an…

For an element $a$ of an integral domain D under an equivalence relation \tau, the \tau-factorization of a is defined as \lambda a_1 a_2... a_k, where \lambda is a unit in D and a_i \tau a_j for all i, j. An irreducible element has no…

Let k be a field and A the n-Kronecker algebra, this is the path algebra of the quiver with 2 vertices, a source and a sink, and n arrows from the source to the sink. It is well-known that the dimension vectors of the indecomposable…

In this paper, we calculate the space $Ext^1_{GL(n)}(L_n(\lambda),L_n(\mu))$, where GL(n) is the general linear group of degree $n$ over an algebraically closed field of positive characteristic, $L_n(\lambda)$ and $L_n(\mu)$ are rational…

This article gives the structure of all projective indecomposable modules in blocks with non-cyclic defect group for $n\leq 11$, and almost all in the case of $n=12$, leaving four simple modules for $p=2$ and one simple module for $p=3$.