Solvable Hopf algebras and their twists

Miriam Cohen; Sara Westreich

doi:10.1016/j.jalgebra.2019.12.004

Solvable Hopf algebras and their twists

Miriam Cohen, Sara Westreich

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We show that for any solvable group G and a Drinfel'd twist J, kG^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.

Original language	English
Pages (from-to)	165-176
Number of pages	12
Journal	Journal of Algebra
Volume	549
DOIs	https://doi.org/10.1016/j.jalgebra.2019.12.004
State	Published - 1 May 2020

Keywords

Drinfel'd twist
Integrals for Hopf algebras
Left coideals subalgebras
Normal left coideal subalgebra
Quantum commutativity
Quasitriangular Hopf algebras
Solvable Hopf algebras
Solvable groups

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2019.12.004

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abstract = "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 [2]. 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.",

keywords = "Drinfel'd twist, Integrals for Hopf algebras, Left coideals subalgebras, Normal left coideal subalgebra, Quantum commutativity, Quasitriangular Hopf algebras, Solvable Hopf algebras, Solvable groups",

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AB - 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 [2]. 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.

KW - Drinfel'd twist

KW - Integrals for Hopf algebras

KW - Left coideals subalgebras

KW - Normal left coideal subalgebra

KW - Quantum commutativity

KW - Quasitriangular Hopf algebras

KW - Solvable Hopf algebras

KW - Solvable groups

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VL - 549

SP - 165

EP - 176

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Solvable Hopf algebras and their twists

Abstract

Keywords

ASJC Scopus subject areas

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