Gelfand-kirillov dimension of cosemisimple hopf algebras

Alexandru Chirvasitu; Chelsea Walton; Xingting Wang

doi:10.1090/proc/14616

Gelfand-kirillov dimension of cosemisimple hopf algebras

Alexandru Chirvasitu
, Chelsea Walton
, Xingting Wang

Mathematics

University of Illinois at Urbana-Champaign
Howard University

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

3 Scopus citations

Abstract

In this note, we compute the Gelfand-Kirillov dimension of cosemisimple Hopf algebras that arise as deformations of a linearly reductive algebraic group. Our work lies in a purely algebraic setting and generalizes results of Goodearl-Zhang (2007), of Banica-Vergnioux (2009), and of D'Andrea-Pinzari- Rossi (2017).

Original language	English
Pages (from-to)	4665-4672
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	11
DOIs	https://doi.org/10.1090/proc/14616
State	Published - 2019

Keywords

Cosemisimple Hopf algebra
Gelfand-Kirillov dimension
Grothendieck semiring
Linearly reductive algebraic group

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10.1090/proc/14616

Cite this

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abstract = "In this note, we compute the Gelfand-Kirillov dimension of cosemisimple Hopf algebras that arise as deformations of a linearly reductive algebraic group. Our work lies in a purely algebraic setting and generalizes results of Goodearl-Zhang (2007), of Banica-Vergnioux (2009), and of D'Andrea-Pinzari- Rossi (2017).",

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AU - Walton, Chelsea

AU - Wang, Xingting

PY - 2019

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N2 - In this note, we compute the Gelfand-Kirillov dimension of cosemisimple Hopf algebras that arise as deformations of a linearly reductive algebraic group. Our work lies in a purely algebraic setting and generalizes results of Goodearl-Zhang (2007), of Banica-Vergnioux (2009), and of D'Andrea-Pinzari- Rossi (2017).

AB - In this note, we compute the Gelfand-Kirillov dimension of cosemisimple Hopf algebras that arise as deformations of a linearly reductive algebraic group. Our work lies in a purely algebraic setting and generalizes results of Goodearl-Zhang (2007), of Banica-Vergnioux (2009), and of D'Andrea-Pinzari- Rossi (2017).

KW - Cosemisimple Hopf algebra

KW - Gelfand-Kirillov dimension

KW - Grothendieck semiring

KW - Linearly reductive algebraic group

UR - https://www.scopus.com/pages/publications/85073036692

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DO - 10.1090/proc/14616

M3 - Article

AN - SCOPUS:85073036692

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

Gelfand-kirillov dimension of cosemisimple hopf algebras

Abstract

Keywords

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