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<p><i>ı</i>Quantum groups, arising from quantum symmetric pairs with Satake diagrams (diagrams with involutions) as the inputs, are coideal subalgebras of quantum groups. By considering quivers with involutions, Lu and Wang (2022) constructed <i>ı</i>Hall algebras to realize <i>ı</i>quantum groups. In this paper, we generalize the above constructions to diagrams with automorphisms. We introduce the quasi <i>ı</i>quantum groups from diagrams with automorphisms <i>ϱ</i>. For a quiver with automorphisms <i>ϱ</i>, the <i>ϱ</i>quiver algebra is defined, and its twisted semi-derived Ringel-Hall algebra (called quasi <i>ı</i>Hall algebra) is used to realize the quasi <i>ı</i>quantum group. For <i>ϱ</i> with an odd period, the derived Hall algebra is isomorphic to the quotient of twisted quasi <i>ı</i>Hall algebra by doing central reduction.</p>

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Quasi ıHall algebras of quivers with automorphisms

  • 期刊论文

  • 发表日期：

    2026年5月14日

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  • Ming Lu,
  • Fengjun Shi

摘要

ıQuantum groups, arising from quantum symmetric pairs with Satake diagrams (diagrams with involutions) as the inputs, are coideal subalgebras of quantum groups. By considering quivers with involutions, Lu and Wang (2022) constructed ıHall algebras to realize ıquantum groups. In this paper, we generalize the above constructions to diagrams with automorphisms. We introduce the quasi ıquantum groups from diagrams with automorphisms ϱ. For a quiver with automorphisms ϱ, the ϱquiver algebra is defined, and its twisted semi-derived Ringel-Hall algebra (called quasi ıHall algebra) is used to realize the quasi ıquantum group. For ϱ with an odd period, the derived Hall algebra is isomorphic to the quotient of twisted quasi ıHall algebra by doing central reduction.