Generalized negligible morphisms and their tensor ideals

• Thorsten Heidersdorf ^[2] ; Hans Wenzl ^[1]
  1. [1] University of California System

     University of California System

     Estados Unidos

     
  2. [2] Universität Bonn, Alemania
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 2, 2022
• Idioma: inglés
• Enlaces
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• Resumen

  • We introduce a generalization of the notion of a negligible morphism and study the associated tensor ideals and thick ideals. These ideals are defined by considering deformations of a given monoidal category C over a local ring R. If the maximal ideal of R is generated by a single element, we show that any thick ideal of C admits an explicitly given modified trace function. As examples we consider various Deligne categories and the categories of tilting modules for a quantum group at a root of unity and for a semisimple, simply connected algebraic group in prime characteristic. We prove an elementary geometric description of the thick ideals in quantum type A and propose a similar one in the modular case.