On the Ringel–Hall Algebra of the Gentle One-Cycle Algebra Λ( n− 1, 1,1)

It is shown that the gentle one-cycle algebra [Formula: see text] has Hall polynomials. The Hall polynomials are explicitly given for all triples of indecomposable modules, and as a consequence, the Ringel–Hall Lie algebra of [Formula: see text] is shown to be isomorphic to its Riedtmann Lie algebra.

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Publication Details

Journal
Algebra Colloquium
Published
2026-05-13
DOI
https://doi.org/10.1142/s1005386726000283
Primary Topic
Algebraic structures and combinatorial models
Type
article
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0.00
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article

On the Ringel–Hall Algebra of the Gentle One-Cycle Algebra Λ( n− 1, 1,1)

Dong Yang, Hui Chen
Algebra Colloquium
Algebraic structures and combinatorial models
article

On the Ringel–Hall Algebra of the Gentle One-Cycle Algebra Λ( n− 1, 1,1)

Dong Yang, Hui Chen
article en

Abstract

It is shown that the gentle one-cycle algebra [Formula: see text] has Hall polynomials. The Hall polynomials are explicitly given for all triples of indecomposable modules, and as a consequence, the Ringel–Hall Lie algebra of [Formula: see text] is shown to be isomorphic to its Riedtmann Lie algebra.

Algebra ColloquiumVol. 33(02)
Nanjing Medical University (CN), Nanjing University (CN)
Openalex Percentile: Top 4%
Algebraic structures and combinatorial models
DOISourceOpenAlex
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On the Ringel–Hall Algebra of the Gentle One-Cycle Algebra Λ( n− 1, 1,1) — Dong Yang, Hui Chen · Algebra Colloquium (2026) | TGRS Research Map | TGRS