摘要
Let A be a bornological quantum group and R a bornological algebra. If R is an essential A-module, then there is a unique extension to M（A）-module with 1x = x. There is a one-to-one corresponding relationship between the actions of A and the coactions of . If R is a Galois object for A, then there exists a faithful δ-invariant functional on R. Moreover,the Galois objects also have modular properties such as algebraic quantum groups. By constructing the comultiplication Δ,counit ε, antipode S and invariant functional φ onR×R, R×R can be considered as a bornological quantum group.
设A为bornological量子群,R为bornological代数.如果R为essential A-模,那么R可以扩张为M(A)-模并且满足1x=x.A上的作用与上的余作用之间有一个一一对应的关系.若R是A上的Galois对象,则R上存在一个忠实的δ-不变泛函,且拥有类似于代数量子群的modular性质.最后,通过构造RR上的余乘Δ、余单位ε、対极S和不变泛函φ,使之成为bornological量子群.
