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<p>Using Hernandez–Leclerc’s isomorphism between the derived Hall algebra of a representation-finite quiver <i>Q</i> and the quantum Grothendieck ring of the quantum loop algebra of the Dynkin type of <i>Q</i>, we lift the (quantum) cluster algebra structure of the quantum Grothendieck ring to the semi-derived Hall algebra, introduced by Gorsky, of the category of bounded complexes of projective modules over the path algebra of <i>Q</i>.</p>

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A Quantum Cluster Algebra Structure on the Semi-Derived Hall Algebra

  • 期刊论文

  • 发表日期：

    2026年3月13日

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  • Alessandro Contu

摘要

Using Hernandez–Leclerc’s isomorphism between the derived Hall algebra of a representation-finite quiver Q and the quantum Grothendieck ring of the quantum loop algebra of the Dynkin type of Q, we lift the (quantum) cluster algebra structure of the quantum Grothendieck ring to the semi-derived Hall algebra, introduced by Gorsky, of the category of bounded complexes of projective modules over the path algebra of Q.