Twisted bi-symplectic structure on Koszul twisted Calabi-Yau algebras

• Xiaojun Chen ^[1] ; Alimjon Eshmatov ^[2] ; Farkhod Eshmatov ^[4] ; Leilei Liu ^[3]
  1. [1] Sichuan University

     Sichuan University

     China

     
  2. [2] University of Toledo

     University of Toledo

     City of Toledo, Estados Unidos

     
  3. [3] Sun Yat-sen University

     Sun Yat-sen University

     China

     
  4. [4] AKFA University, Uzbekistan

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 3, 2022
• Idioma: inglés
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• Resumen

  • For a Koszul Artin-Schelter regular algebra (also called twisted Calabi-Yau algebra), we show that it has a “twisted" bi-symplectic structure, which may be viewed as a noncommutative and twisted analog of the shifted symplectic structure introduced by Pantev, Toën, Vaquié and Vezzosi. This structure gives a quasi-isomorphism between the tangent complex and the twisted cotangent complex of the algebra, and may be viewed as a DG enhancement of Van den Bergh’s noncommutative Poincaré duality;

    it also induces a twisted symplectic structure on its derived representation schemes.