We show that for any solvable group G and a Drinfel'd twist J, kGJ is solvable in the sense of the intrinsic definition of solvability given in . More generally, if a Hopf algebra H has a normal solvable series so does HJ. Furthermore, while solvable groups are defined as having certain commutative quotients, quasitriangular normally solvable Hopf algebras have appropriate quantum commutative quotients. We end with a detailed example.
|Number of pages||12|
|Journal||Journal of Algebra|
|State||Published - 1 May 2020|
Bibliographical notePublisher Copyright:
© 2019 Elsevier Inc.
- Drinfel'd twist
- Integrals for Hopf algebras
- Left coideals subalgebras
- Normal left coideal subalgebra
- Quantum commutativity
- Quasitriangular Hopf algebras
- Solvable Hopf algebras
- Solvable groups