Related papers: Indecomposables live in all smaller lengths

We study the degree of irreducible morphisms in any Auslander-Reiten component of a finite dimensional algebra over an algebraically closed field. We give a characterization for an irreducible morphism to have finite left (or right) degree.…

In this paper we show that any irreducible finite dimensional representation of $SL_{n+1}$ remains indecomposable if restricted to n--dimensional abelian subalgebras spanned by simple root vectors.

For any truncated path algebra $\Lambda$ of a quiver, we classify, by way of representation-theoretic invariants, the irreducible components of the parametrizing varieties $\mathbf{Rep}_{\mathbf{d}}(\Lambda)$ of the $\Lambda$-modules with…

We prove that if $A$ is a string algebra then there are not three irreducible morphisms between indecomposable $A$-modules such that its composition belongs to $\Re^{6} \backslash \Re^{7}$, whenever the compositions of two of them are not…

The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…

Let $\bbk$ be an algebraically closed field of prime characteristic $p$. If $p$ does not divide $n$, irreducible modules over $\frak {sl}_n$ for regular and subregular nilpotent representations have already known(see \cite{Jan2} and…

Given a finite dimensional algebra $\Lambda$, we show that a frequently satisfied finiteness condition for the category ${\cal P}^{\infty}(\Lambda\rm{-mod})$ of all finitely generated (left) $\Lambda$-modules of finite projective dimension,…

Let $R$ be an affine algebra over an algebraically closed field of characteristic $0$ with dim$(R)=n$. Let $P$ be a projective $A=R[T_1,\cdots,T_k]$-module of rank $n$ with determinant $L$. Suppose $I$ is an ideal of $A$ of height $n$ such…

The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…

It is shown that for the restricted Zassenhaus algebra $\mathfrak{W}=\mathfrak{W}(1,n)$, $n>1$, defined over an algebraically closed field $\mathbb{F}$ of characteristic 2 any projective indecomposable restricted $\mathfrak{W}$-module has…

We present some results about the irreducible representations appearing in the exterior algebra $\Lambda \mathfrak{g}$, where $ \mathfrak{g}$ is a simple Lie algebra over $\mathbb{C}$. For Lie algebras of type $B$, $C$ or $D$ we prove that…

Understanding the structure of indecomposable $n$-dimensional persistence modules is a difficult problem, yet is foundational for studying multipersistence. To this end, Buchet and Escolar showed that any finitely presented rectangular…

Let L be a Leibniz algebra of dimension n. I prove the existence of a faithful L-module of dimension less than or equal to n+1.

Indecomposable continua with one composant are $\textit{large}$ in the sense of being non-metrisable. We adapt the method of Smith $[18]$ to construct an example which is $\textit{small}$ in the sense of being separable.

By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra $L(\Lambda)$ generated by indecomposable constructible sets in the varieties of modules for any finite dimensional $\mathbb{C}$-algebra $\Lambda.$ We…

Let $\mathfrak g$ be a semisimple Lie algebra and $\mathfrak k\subset\mathfrak g$ be a reductive in $\mathfrak g$ subalgebra. A $(\mathfrak g, \mathfrak k)$-module is a $\mathfrak g$-module which after restriction to $\mathfrak k$ becomes a…

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…

We construct a new class of finite dimensional indecomposable representations of simple superalgebras which may explain, in a natural way, the existence of the heavier elementary particles. In type I Lie superalgebras sl(m/n) and osp(2/2n),…

We prove that if a separable II$_1$ factor $M$ is existentially closed, then every $M$-bimodule is weakly contained in the trivial $M$-bimodule, $\text{L}^2(M)$, and, equivalently, every normal completely positive map on $M$ is a pointwise…

A recent work by Lesnick and Wright proposed a visualisation of $2$D persistence modules by using their restrictions onto lines, giving a family of $1$D persistence modules. We give a constructive proof that any $1$D persistence module with…