What question did this study set out to answer?

To investigate the noncommutative singularity theory related to the double A_n quiver and its implications in algebraic geometry and representation theory.

March 28, 2026Mathematische ZeitschriftOpen Access

Local forms for the double Aₙ quiver

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Authors

HZHao ZhangNortheastern Illinois University

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Implication

Explores noncommutative singularity theory in the double A_n quiver, revealing important algebraic connections.

Key Points

To investigate the noncommutative singularity theory related to the double A_n quiver and its implications in algebraic geometry and representation theory.
Defined various intrinsic forms of Type A potentials on double A_n quiver Q_n.
Proved a monomialization result for expressing potentials.
Established correspondence between Type A potentials and crepant resolutions of cA_n singularities.
Classified Type A potentials for n ≤ 3, including those with finite-dimensional Jacobi algebras.
Demonstrated a clear monomial representation of Type A potentials.
Confirmed that Type A potentials correspond to specific crepant resolutions of singularities.
Achieved a full classification of Type A potentials up to isomorphism for n ≤ 3.
Outlined algebraic contributions relevant to tame algebras of quaternion type.

Cite This Study

Hao Zhang (2026) studied this question.

synapsesocial.com/papers/69c7723a8bbfbc51511e290d https://doi.org/10.1007/s00209-026-04003-w

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Local forms for the double Aₙ quiver

Discussion

Member takes

Implication

Key Points

Cite This Study

Local forms for the double Aₙ quiver

Discussion

Member takes

Implication

Key Points

Cite This Study

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