Results 1 to 10 of about 2,837 (110)
On the number of terms in the middle of almost split sequences over cycle-finite artin algebras [PDF]
Open Mathematics, 2014 We prove that the number of terms in the middle of an almost split sequence in the module category of a cycle-finite artin algebra is bounded by ...
Malicki Piotr +2 more
doaj +3 more sources
On the Auslander-Reiten Quiver of the Representations of an Infinite Quiver [PDF]
Algebras and Representation Theory, 2012 Let Q be a strongly locally finite quiver and denote by rep(Q) the category of locally finite dimensional representations of Q over some fixed field k. The main purpose of this paper is to get a better understanding of rep(Q) by means of its Auslander-Reiten quiver. To achieve this goal, we define a category C(Q) which is a full, abelian and Hom-finite
Charles Paquette
exaly +4 more sources
On uniserial modules in the Auslander–Reiten quiver
Journal of Algebra, 2008 This article begins the study of irreducible maps involving finite-dimensional uniserial modules over finite-dimensional associative algebras. We work on the classification of irreducible maps between two uniserials over triangular algebras, and give estimates for the number of middle terms of an almost split sequence with a uniserial end term.
Boldt, Axel, Mojiri, Ahmad
exaly +4 more sources
The Auslander–Reiten Quiver of a Poincaré Duality Space
Algebras and Representation Theory, 2006 In a previous paper, math.AT/0304079, Auslander-Reiten triangles and quivers were introduced into algebraic topology. This paper shows that over a Poincare duality space, each component of the Auslander-Reiten quiver is isomorphic to ZA_{\infty}.
exaly +4 more sources
Mathematics, 2022 The four subspace problem is a known matrix problem, which is equivalent to determining all the indecomposable representations of a poset consisting of four incomparable points.
Agustín Moreno Cañadas +2 more
doaj +1 more source
On Auslander-Reiten components of algebras without external short paths [PDF]
, 2011 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 Auslander-Reiten quiver ...
Jaworska, Alicja +2 more
core +4 more sources
Representation theory of partial relation extensions [PDF]
, 2019 Let C be a finite dimensional algebra of global dimension at most two. A partial relation extension is any trivial extension of C by a direct summand of its relation C-C-bimodule.
Assem, Ibrahim +4 more
core +4 more sources
Coxeter elements and periodic Auslander–Reiten quiver
Journal of Algebra, 2010 27 pages, 10 figures.
Kirillov, A., Thind, J.
openaire +3 more sources
Auslander?Reiten Quivers and the Coxeter Complex [PDF]
Algebras and Representation Theory, 2005 Let Q be a quiver of type ADE. We construct the corresponding Auslander-Reiten quiver as a topological complex inside the Coxeter complex associated with the underlying Dynkin diagram. We use the notion of chamber weights coming from the theory of the canonical basis of quantized envelopping algebras, and show this set has a special linearity property ...
openaire +5 more sources
Invariant Subspaces of Nilpotent Linear Operators. I [PDF]
, 2006 Let $k$ be a field. We consider triples $(V,U,T)$, where $V$ is a finite dimensional $k$-space, $U$ a subspace of $V$ and $T \:V \to V$ a linear operator with $T^n = 0$ for some $n$, and such that $T(U) \subseteq U$. Thus, $T$ is a nilpotent operator on $
Bourbaki N. +3 more
core +3 more sources