scholarly journals Diagrammatic morphisms between indecomposable modules of Ūq(𝔰𝔩2)

2020 ◽  
Vol 31 (02) ◽  
pp. 2050016
Author(s):  
Stephen T. Moore
Keyword(s):  
Indecomposable Modules ◽  
Indecomposable Representations

We give diagrammatic formulae for morphisms between indecomposable representations of [Formula: see text] appearing in the decomposition of [Formula: see text], including projections and second endomorphisms on projective indecomposable representations.

scholarly journals On the Number of Absolutely Indecomposable Representations of a Quiver

1999 ◽  
Vol 221 (1) ◽  
pp. 29-49 ◽  
Author(s):  
Bert Sevenhant ◽  
Michel Van Den Bergh
Keyword(s):  
Indecomposable Representations

scholarly journals Indecomposable modules over pure semisimple hereditary rings

2012 ◽  
Vol 371 ◽  
pp. 577-595 ◽  
Author(s):  
Nguyen Viet Dung ◽  
José Luis García
Keyword(s):  
Indecomposable Modules

scholarly journals Indecomposable modules over one-dimensional Noetherian rings

2007 ◽  
Vol 208 (2) ◽  
pp. 739-760 ◽  
Author(s):  
Meral Arnavut ◽  
Melissa Luckas ◽  
Sylvia Wiegand
Keyword(s):  
Noetherian Rings ◽  
Indecomposable Modules ◽  
One Dimensional

Completely Indecomposable Modules

1949 ◽  
Vol 1 (2) ◽  
pp. 125-152 ◽  
Author(s):  
Ernst Snapper
Keyword(s):  
Abelian Group ◽  
Commutative Ring ◽  
Chain Condition ◽  
Indecomposable Module ◽  
Unit Element ◽  
Indecomposable Modules ◽  
Operator Domain ◽  
Unit Operator ◽  
Ascending Chain Condition

The purpose of this paper is to investigate completely indecomposable modules. A completely indecomposable module is an additive abelian group with a ring A as operator domain, where the following four conditions are satisfied.1-1. A is a commutative ring and has a unit element which is unit operator for .1-2. The submodules of satisfy the ascending chain condition. (Submodule will always mean invariant submodule.)

scholarly journals Kac Polynomials for Canonical Algebras

2017 ◽  
Vol 2019 (13) ◽  
pp. 3981-4003
Author(s):  
Pierre-Guy Plamondon ◽  
Olivier Schiffmann
Keyword(s):  
Finite Field ◽  
Dimension Vector ◽  
Indecomposable Representations ◽  
Moduli Stacks ◽  
Fixed Dimension ◽  
Canonical Algebra

Abstract We prove that the number of geometrically indecomposable representations of fixed dimension vector $\mathbf{d}$ of a canonical algebra $C$ defined over a finite field $\mathbb{F}_q$ is given by a polynomial in $q$ (depending on $C$ and $\mathbf{d}$). We prove a similar result for squid algebras. Finally, we express the volume of the moduli stacks of representations of these algebras of a fixed dimension vector in terms of the corresponding Kac polynomials.

On representations of graphs of type A

1992 ◽  
Vol 439 (1907) ◽  
pp. 687-690
Keyword(s):  
Finite Number ◽  
Type A ◽  
Indecomposable Representations

We investigate the number of orbits in a variety Λ v associated to Dynkin graphs of type A n as defined by G. Lusztig. For n < 4, we show that there is only a finite number of indecomposable representations in Λ v up to isomorphism. This implies that Λ v consists of finitely many orbits for any V . For each n > 4, we show that there exist V for which Λ v contains infinitely many orbits.

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