The field of quantum GL(N,CC) in the C ∗ -algebraic setting

• Kenny De Commer ^[1] ; Matthias Floré ^[1]
  1. [1] Vrije Universiteit Brussel

     Vrije Universiteit Brussel

     Arrondissement Brussel-Hoofdstad, Bélgica

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 1, 2019
• Idioma: inglés
• DOI: 10.1007/s00029-019-0456-0
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• Resumen

  • Given a unital ∗ -algebra A together with a suitable positive filtration of its set of irreducible bounded representations, one can construct a C ∗ -algebra A0 with a dense two-sided ideal Ac such that A maps into the multiplier algebra of Ac . When the filtration is induced from a central element in A , we say that A is an s ∗ -algebra. We also introduce the notion of R -algebra relative to a commutative s ∗ -algebra R , and of Hopf R -algebra. We formulate conditions such that the completion of a Hopf R -algebra gives rise to a continuous field of Hopf C ∗ -algebras over the spectrum of R0 . We apply the general theory to the case of quantum GL(N,C) as constructed from the FRT-formalism.