Zariski cancellation problem for noncommutative algebras

• Jason Bell ^[1] ; James J. Zhang ^[2]
  1. [1] University of Waterloo

     University of Waterloo

     Canadá

     
  2. [2] University of Washington

     University of Washington

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 3, 2017, págs. 1709-1737
• Idioma: inglés
• DOI: 10.1007/s00029-017-0317-7
• Enlaces
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• Resumen

  • A noncommutative analogue of the Zariski cancellation problem asks whether A[x] ∼= B[x] implies A ∼= B when A and B are noncommutative algebras.

    We resolve this affirmatively in the case when A is a noncommutative finitely generated domain over the complex field of Gelfand–Kirillov dimension two. In addition, we resolve the Zariski cancellation problem for several classes of Artin–Schelter regular algebras of higher Gelfand–Kirillov dimension.