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

Kenny De Commer, Matthias Floré

• 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.