Weak Bialgebras of Fractions

Abstract

We construct the algebra of fractions of a Weak Bialgebra relative to a suitable denominator set of group-like elements that is `almost central', a condition we introduce in the present article which is sufficient in order to guarantee existence of the algebra of fractions and to render it a Weak Bialgebra. The monoid of all group-like elements of a coquasi-triangular Weak Bialgebra, for example, forms a suitable set of denominators as does any monoid of central group-like elements of an arbitrary Weak Bialgebra. We use this technique in order to construct new Weak Bialgebras whose categories of finite-dimensional comodules relate to SL2-fusion categories in the same way as GL(2) relates to SL(2).