Generators for K-theoretic Hall algebras of quivers with potential

• Tudor Pădurariu ^[1]
  1. [1] Columbia University

     Columbia University

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 1, 2024, 37 págs.
• Idioma: inglés
• DOI: 10.1007/s00029-023-00891-6
• Enlaces
  • Texto completo
• Resumen

  • K-theoretic Hall algebras (KHAs) of quivers with potential (Q, W) are a generalization of preprojective KHAs of quivers, which are conjecturally positive parts of the Okounkov–Smironov quantum affine algebras. In particular, preprojective KHAs are expected to satisfy a Poincaré–Birkhoff–Witt theorem. We construct semi-orthogonal decompositions of categorical Hall algebras using techniques developed by HalpernLeistner, Ballard–Favero–Katzarkov, and Špenko–Van den Bergh. For a quotient of KHA(Q, W)Q, we refine these decompositions and prove a PBW-type theorem for it. The spaces of generators of KHA(Q, 0)Q are given by (a version of) intersection K-theory of coarse moduli spaces of representations of Q.

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