In this paper we introduce a notion of divisibility and primality on k-ary trees and we nd a relation between indecomposable preex code and prime trees. This relation allows to work on trees instead than directly on preex codes. In this way we can prove a density theorem for indecomposable preex codes and we can give an algorithm to test the indecomposability of a maximal preex code.

We categorify Lusztig’s U̇ – a version of the quantized enveloping algebra Uq(sl2). Using a graphical calculus a 2-category U̇ is constructed whose split Grothendieck ring is isomorphic to the algebra U̇. The indecomposable morphisms of this 2-category lift Lusztig’s canonical basis, and the Homs between 1-morphisms are graded lifts of a semilinear form defined on U̇. Graded lifts of various homomo...

We write down one-to-one mappings between the singular vectors of the Neveu-Schwarz N=2 superconformal algebra and 16 + 16 types of singular vectors of the Topological and of the Ramond N=2 superconformal algebras. As a result one obtains construction formulae for the latter using the construction formulae for the Neveu-Schwarz singular vectors due to Dörrzapf. The indecomposable singular vecto...

The Auslander-Reiten quiver of a finite-dimensional associative algebra A encodes information about the indecomposable finite-dimensional representations of A and their homomorphisms. A component of the AuslanderReiten quiver is called preprojective if it does not admit oriented cycles and each of its modules can be shifted into a projective module using the AuslanderReiten translation. Preproj...

Let A be a hereditary algebra over an algebraically closed field k andA(m) be them-replicated algebra of A. Given an A(m)-module T , we denote by δ(T ) the number of non isomorphic indecomposable summands of T . In this paper, we prove that a partial tilting A(m)module T is a tilting A(m)-module if and only if δ(T ) = δ(A(m)), and that every partial tilting A(m)-module has complements. As an ap...

Bernstein algebras were introduced by Holgate [6] as an algebraic formulation of the problem of classifying the stationary evolution operators in genetics (see [8]). Since then, many authors have contributed to the study of these algebras, and there is a fairly extensive bibliography on the subject. Known results include classification theorems for sorre types of Bernstein algebras (for instanc...

This paper presents a geometric model of the Auslander–Reiten quiver type A together with stability function for which all indecomposable modules are stable. We also introduce new Catalan object we call maximal almost rigid representation. show that its endomorphism algebra is tilted A. define partial order on set representations and use our to this Cambrian lattice.

We introduce the marked Brauer algebra and the marked Brauer category. These generalize the analogous constructions for the ordinary Brauer algebra to the setting of a homogeneous bilinear form on a Z2-graded vector space. We classify the simple modules of the marked Brauer algebra over any field of characteristic not two. Under suitable assumptions we show that the marked Brauer algebra is in ...

In this paper we develop combinatorial techniques for the case of string algebras with aim to give a characterization complexes infinite minimal projective resolution. These will be called periodic complexes. As consequence characterization, two important applications. The first one, is sufficient condition algebra have global dimension. second exhibit class indecomposable objects in derived ca...