Modules of indecompasable Representation of Quivers and the generators of associated Lie algebra

Yuichi Miyake

doi:10.48617/etd.1472

January 1, 2025Open Access

Modules of indecompasable Representation of Quivers and the generators of associated Lie algebra

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Key Points

The aim is to explore the relationship between indecomposable representations of quivers and the generators of the associated Lie algebra.
Review of Gabriel's results on ADE Dynkin quivers and their positive root systems.
Examination of exact sequences of modules related to quivers.
Analysis of observations on orientation of simply-laced quivers, particularly type A.
Identified critical connections between the representation of quivers and their associated Lie algebra generators.
Demonstrated the role of positive root systems in understanding these relationships.
Illustrated the significance of exact sequences of modules in the context of Lie algebra.

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Implication

This expository work explores the connection between indecomposable representations and Lie algebra generators using quivers, suggesting significant theoretical implications.

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Yuichi Miyake (2025) studied this question.

synapsesocial.com/papers/6992b3ca9b75e639e9b08999 https://doi.org/10.48617/etd.1472

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Modules of indecompasable Representation of Quivers and the generators of associated Lie algebra

Key Points

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Modules of indecompasable Representation of Quivers and the generators of associated Lie algebra

Key Points

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Implication

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