Pre-weight structures, pseudo-identities and canonical derived equivalences

• Xiao-Wu Chen ^[1]
  1. [1] University of Science and Technology of China

     University of Science and Technology of China

     China

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 5, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01106-w
• Enlaces
  • Texto completo
• Resumen

  • We introduce the notion of pre-weight structure on a triangulated category and study the corresponding pseudo-identities.We propose the notion of canonical derived equivalence between algebras that are not necessarily flat, which is associated to a tilting complex. In the flat situation, canonical derived equivalences coincide with standard derived equivalences in the sense of Rickard. We prove that any derived equivalence starting from a hereditary algebra is canonical. The key tool is a general factorization theorem: any derived equivalence is uniquely factorized as a pseudo-identity followed by a canonical derived equivalence.

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