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Rationality of the Hilbert series of Hopf-invariants of free algebras


Authors: Vitor O. Ferreira and Lucia S. I. Murakami
Journal: Proc. Amer. Math. Soc. 142 (2014), 821-826
MSC (2010): Primary 16S10, 16T05, 16W22, 15A72
DOI: https://doi.org/10.1090/S0002-9939-2013-11830-7
Published electronically: December 6, 2013
MathSciNet review: 3148516
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the subalgebra of invariants of a free associative algebra of finite rank under a linear action of a semisimple Hopf algebra has a rational Hilbert series with respect to the usual degree function whenever the ground field has zero characteristic.


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Additional Information

Vitor O. Ferreira
Affiliation: Department of Mathematics, Institute of Mathematics and Statistics, University of São Paulo, Caixa Postal 66281, São Paulo - SP, 05314-970, Brazil
Email: vofer@ime.usp.br

Lucia S. I. Murakami
Affiliation: Department of Mathematics, Institute of Mathematics and Statistics, University of São Paulo, Caixa Postal 66281, São Paulo - SP, 05314-970, Brazil
Email: ikemoto@ime.usp.br

DOI: https://doi.org/10.1090/S0002-9939-2013-11830-7
Keywords: Free associative algebra, Hopf algebra actions, invariants
Received by editor(s): May 26, 2011
Received by editor(s) in revised form: April 13, 2012
Published electronically: December 6, 2013
Additional Notes: The first author was partially supported by CNPq (Grant 308163/2007-9) and by FAPESP (Projeto Temático 2009/52665-0).
The second author was partially supported by FAPESP (Projeto Temático 2010/50347-9).
Communicated by: Harm Derksen
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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