Results 11 to 20 of about 931 (51)

Linear versus set valued Kronecker representations

, 2016
A set valued representation of the Kronecker quiver is nothing but a quiver. We apply the forgetful functor from vector spaces to sets and compare linear with set valued representations of the Kronecker quiver.Comment: 7 ...
Großblotekamp, Kay, Krause, Henning
core   +1 more source

Indecomposables live in all smaller lengths

, 2010
Let $\Lambda$ be a finite-dimensional $k$-algebra with $k$ algebraically closed. Bongartz has recently shown that the existence of an indecomposable $\Lambda$-module of length $n > 1$ implies that also indecomposable $\Lambda$-modules of length $n-1 ...
Ringel, Claus Michael
core   +1 more source

Extensions of Simple Modules and the Converse of Schur's Lemma

, 2009
The converse of Schur's lemma (or CSL) condition on a module category has been the subject of considerable study in recent years. In this note we extend that work by developing basic properties of module categories in which the CSL condition governs ...
Marks, Greg, Schmidmeier, Markus
core   +1 more source

Resolved-sideband cooling and measurement of a micromechanical oscillator close to the quantum limit

, 2009
The observation of quantum phenomena in macroscopic mechanical oscillators has been a subject of interest since the inception of quantum mechanics. Prerequisite to this regime are both preparation of the mechanical oscillator at low phonon occupancy and ...
Anetsberger, Georg, Arcizet, Olivier, Kippenberg, Tobias J., Rivière, Rémi, Schließer, Albert   +4 more
core   +1 more source

Mutation graph of support $\tau $ -tilting modules over a skew-gentle algebra

Forum of Mathematics, Sigma
Let $\mathcal {D}$ be a Hom-finite, Krull-Schmidt, 2-Calabi-Yau triangulated category with a rigid object R. Let $\Lambda =\operatorname {End}_{\mathcal {D}}R$ be the endomorphism algebra of R. We introduce the notion of mutation of maximal
Ping He, Yu Zhou, Bin Zhu
doaj   +1 more source

A smooth compactification of spaces of stability conditions: the case of the $A_{n}$ -quiver

Forum of Mathematics, Sigma
We propose a notion of multi-scale stability conditions with the goal of providing a smooth compactification of the quotient of the space of projectivized Bridgeland stability conditions by the group of autoequivalence.
Anna Barbieri, Martin Möller, Jeonghoon So   +2 more
doaj   +1 more source

Singularity categories of gentle algebras

, 2014
We determine the singularity category of an arbitrary finite dimensional gentle algebra $\Lambda$. It is a finite product of $n$-cluster categories of type $\mathbb{A}_{1}$.
Kalck, Martin
core   +1 more source

The geometry of uniserial representations of algebras II. Alternate viewpoints and uniqueness [PDF]

, 2014
We provide two alternate settings for a family of varieties modeling the uniserial representations with fixed sequence of composition factors over a finite dimensional algebra.
Bongartz, Klaus, Huisgen-Zimmermann, Birge   +1 more
core  

On Hochschild cohomology of a self-injective special biserial algebra obtained by a circular quiver with double arrows

, 2014
We calculate the dimensions of the Hochschild cohomology groups of a self-injective special biserial algebra $\Lambda_{s}$ obtained by a circular quiver with double arrows.
Itaba, Ayako
core   +1 more source

Consistent dimer models on surfaces with boundary

Forum of Mathematics, Sigma
A dimer model is a quiver with faces embedded in a surface. We define and investigate notions of consistency for dimer models on general surfaces with boundary which restrict to well-studied consistency conditions in the disk and torus case.
Jonah Berggren, Khrystyna Serhiyenko
doaj   +1 more source