Galois reconstruction of finite quantum groups

JOURNAL OF ALGEBRA

卷:230

Article

Bichon, J

关键词: quantum groups;    Galois theory;    Tannaka duality;    groups acting on sets;   

DOI  :  10.1006/jabr.2000.8340

来源: Elsevier

【 摘 要 】

Let E be a (small) category and let F: E -->Malg(f) be a functor, where Malg(f) is the category of finite-dimensional measured algebras over a field k (or Frobenius algebras). We construct a universal Hopf algebra A(aug)(F) such that F factorizes through a functor (F) over bar: E --> Mcoalg(f)(A(aut)(F)), where Mcoalg(f)(A(aut)(F)) is the category of finite-dimensional measured A(aut)(F)-comodule algebras. This general reconstruction result allows us to recapture a finite-dimensional Hopf algebra A from the category Mcoalg(f)(A) and the forgetful functor omega: Mcoalg(f)(A) --> Malg(f): we have A congruent to A(aut)(omega). Our universal construction is also done in a C*-algebra framework, and we get compact quantum groups in the sense of Woronowicz. (C) 2000 Academic Press.

【 授权许可】

Free