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Solvable Hopf algebras and their twists
Journal of Algebra ( IF 0.9 ) Pub Date : 2020-05-01 , DOI: 10.1016/j.jalgebra.2019.12.004
Miriam Cohen , Sara Westreich

Abstract We show that for any solvable group G and a Drinfel'd twist J, k G J is solvable in the sense of the intrinsic definition of solvability given in [2] . More generally, if a Hopf algebra H has a normal solvable series so does H J . 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.

中文翻译:

可解的 Hopf 代数及其转折

摘要 我们证明,对于任何可解群 G 和 Drinfel'd 扭曲 J,k GJ 在 [2] 中给出的可解性的内在定义的意义上是可解的。更一般地,如果 Hopf 代数 H 具有正常的可解级数,那么 HJ 也是如此。此外,虽然可解群被定义为具有某些交换商,但拟三角通常可解的 Hopf 代数具有适当的量子交换商。我们以一个详细的例子结束。
更新日期:2020-05-01
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