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

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.