On the Hopf (co)center of a Hopf algebra

Alexandru Chirvasitu; Paweł Kasprzak

doi:10.1016/j.jalgebra.2016.07.002

On the Hopf (co)center of a Hopf algebra

Alexandru Chirvasitu
, Paweł Kasprzak

Mathematics

University of Warsaw

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

3 Scopus citations

Abstract

The notion of Hopf center and Hopf cocenter of a Hopf algebra is investigated by the extension theory of Hopf algebras. We prove that each of them yields an exact sequence of Hopf algebras. Moreover the exact sequences are shown to satisfy the faithful (co)flatness condition. Hopf center and cocenter are computed for U_q(g) and the Hopf algebra Pol(G_q), where G_q is the Drinfeld–Jimbo quantization of a compact semisimple simply connected Lie group G and g is a simple complex Lie algebra.

Original language	English
Pages (from-to)	141-174
Number of pages	34
Journal	Journal of Algebra
Volume	464
DOIs	https://doi.org/10.1016/j.jalgebra.2016.07.002
State	Published - Oct 15 2016

Keywords

Comodule
Hopf center
Hopf cocenter
Monoidal category
Tannaka reconstruction

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10.1016/j.jalgebra.2016.07.002

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abstract = "The notion of Hopf center and Hopf cocenter of a Hopf algebra is investigated by the extension theory of Hopf algebras. We prove that each of them yields an exact sequence of Hopf algebras. Moreover the exact sequences are shown to satisfy the faithful (co)flatness condition. Hopf center and cocenter are computed for Uq(g) and the Hopf algebra Pol(Gq), where Gq is the Drinfeld–Jimbo quantization of a compact semisimple simply connected Lie group G and g is a simple complex Lie algebra.",

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AU - Kasprzak, Paweł

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N2 - The notion of Hopf center and Hopf cocenter of a Hopf algebra is investigated by the extension theory of Hopf algebras. We prove that each of them yields an exact sequence of Hopf algebras. Moreover the exact sequences are shown to satisfy the faithful (co)flatness condition. Hopf center and cocenter are computed for Uq(g) and the Hopf algebra Pol(Gq), where Gq is the Drinfeld–Jimbo quantization of a compact semisimple simply connected Lie group G and g is a simple complex Lie algebra.

AB - The notion of Hopf center and Hopf cocenter of a Hopf algebra is investigated by the extension theory of Hopf algebras. We prove that each of them yields an exact sequence of Hopf algebras. Moreover the exact sequences are shown to satisfy the faithful (co)flatness condition. Hopf center and cocenter are computed for Uq(g) and the Hopf algebra Pol(Gq), where Gq is the Drinfeld–Jimbo quantization of a compact semisimple simply connected Lie group G and g is a simple complex Lie algebra.

KW - Comodule

KW - Hopf center

KW - Hopf cocenter

KW - Monoidal category

KW - Tannaka reconstruction

UR - https://www.scopus.com/pages/publications/84978194577

U2 - 10.1016/j.jalgebra.2016.07.002

DO - 10.1016/j.jalgebra.2016.07.002

M3 - Article

AN - SCOPUS:84978194577

SN - 0021-8693

VL - 464

SP - 141

EP - 174

JO - Journal of Algebra

JF - Journal of Algebra

ER -

On the Hopf (co)center of a Hopf algebra

Abstract

Keywords

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