Algebraic quantum permutation groups. (English) Zbl 1170.16028
S. Wang, [in Commun. Math. Phys. 195, No. 1, 195-211 (1998; Zbl 1013.17008)], constructed universal compact quantum groups acting on \(\{1,\dots,n\}\). In the paper under review, this construction is adapted to produce analogous Hopf algebras over any base field \(k\). It is then proved, when \(k\) has characteristic zero, that the constructed Hopf algebras are the universal cosemisimple Hopf algebras coacting on \(k^n\). Consequences for Hopf algebras having non-ergodic coactions on \(k^n\) are presented, with applications to group gradings on \(k^n\).
Reviewer: Edward S. Letzter (Philadelphia)
MSC:
| 16W30 | Hopf algebras (associative rings and algebras) (MSC2000) |
| 16W35 | Ring-theoretic aspects of quantum groups (MSC2000) |
| 16W50 | Graded rings and modules (associative rings and algebras) |
Keywords:
universal cosemisimple Hopf algebras; diagonal coactions; quantum permutation groups; group gradingsCitations:
Zbl 1013.17008References:
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