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Gelfand-Kirillov dimension of cosemisimple Hopf algebras


Authors: Alexandru Chirvasitu, Chelsea Walton and Xingting Wang
Journal: Proc. Amer. Math. Soc. 147 (2019), 4665-4672
MSC (2010): Primary 16P90, 16T20, 20G42, 16T15
DOI: https://doi.org/10.1090/proc/14616
Published electronically: June 10, 2019
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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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Additional Information

Alexandru Chirvasitu
Affiliation: Department of Mathematics, University at Buffalo, Buffalo, New York 14260
Email: achirvas@buffalo.edu

Chelsea Walton
Affiliation: Department of Mathematics, The University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email: notlaw@illinois.edu

Xingting Wang
Affiliation: Department of Mathematics, Howard University, Washington, District of Columbia 20059
Email: xingting.wang@howard.edu

DOI: https://doi.org/10.1090/proc/14616
Keywords: Cosemisimple Hopf algebra, Gelfand-Kirillov dimension, Grothendieck semiring, linearly reductive algebraic group
Received by editor(s): July 26, 2018
Received by editor(s) in revised form: February 23, 2019
Published electronically: June 10, 2019
Additional Notes: The first and second authors were partially supported by the U.S. National Science Foundation with grants #DMS-1801011 and #DMS-1663775, respectively.
The second author was also supported by a research fellowship from the Alfred P. Sloan foundation.
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2019 American Mathematical Society