Stable homology isomorphisms for the partition and Jones annular algebras

• Guy Boyde ^[1]
  1. [1] Utrecht University

     Utrecht University

     Países Bajos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 5, 2024
• Idioma: inglés
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• Resumen

  • We show that the homology of the Jones annular algebras is isomorphic to that of the cyclic groups below a line of gradient 1/2 We also show that the homology of the partition algebras is isomorphic to that of the symmetric groups below a line of gradient 1, strengthening a result of Boyd–Hepworth–Patzt. Both isomorphisms hold in a range exceeding the stability range of the algebras in question. Along the way, we prove the usual odd-strand and invertible parameter results for the Jones annular algebras.