Weak Bialgebras of fractions

We construct the algebra of fractions of a Weak Bialgebra relative to a suitable denominator set of group-like elements that is , 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 -fusion categories in the same way as relates to .

我们相对于一组合适的类群元素分母集来构造弱双代数的分式代数，也就是说，我们在本文中引入的一个条件，该条件足以保证分式代数的存在并使其成为一个弱双代数。例如，一个余拟三角弱双代数的所有类群元素的幺半群，就像任意弱双代数的中心类群元素的任何幺半群一样，构成了一组合适的分母。我们使用这种技术来构造新的弱双代数，其有限维余模的范畴与 -融合范畴的关系和 与 的关系相同。