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 Management

Ben-Gurion University of the Negev

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

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

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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10.1016/j.jalgebra.2019.12.004

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title = "Solvable Hopf algebras and their twists",

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.",

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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

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

Solvable Hopf algebras and their twists

Abstract

Bibliographical note

Keywords

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