<abstract xmlns="http://www.w3.org/1999/xhtml"> Let k be a finite field and consider the finite dimensional path algebra kQ, where Q is a quiver of tame type i.e. of type Ãn, D̃n,Ẽ6,Ẽ7,Ẽ8. Let H(kQ) be the corresponding Ringel-Hall algebra. We are going to determine the Ringel-Hall numbers of the form FP`XP with P, P` preprojective indecomposables of defect -1 and FI`IX with I, I` preinjective indecomposables of defect 1. It turns out that these numbers are either 1 or 0. </abstract>

Let k be a finite field and consider the finite dimensional path algebra kQ, where Q is a quiver of tame type i.e. of type Ãn, D̃n,Ẽ6,Ẽ7,Ẽ8. Let H(kQ) be the corresponding Ringel-Hall algebra. We are going to determine the Ringel-Hall numbers of the form FP`XP with P, P` preprojective indecomposables of defect -1 and FI`IX with I, I` preinjective indecomposables of defect 1. It turns out that these numbers are either 1 or 0.

On some Ringel-Hall numbers in tame cases

Acta Universitatis Sapientiae, Mathematica

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{"article-title":"On some Ringel-Hall numbers in tame cases"}

Let k be a finite field and consider the finite dimensional path algebra kQ, where Q is a quiver of tame type i.e. of type Ãn, D̃n,Ẽ6,Ẽ7,Ẽ8. Let H(kQ) be the...

On some Ringel-Hall numbers in tame cases

Published Online: Nov 05, 2014

Page range: 61 - 72

Received: Apr 09, 2014

DOI: https://doi.org/10.2478/ausm-2014-0018

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.