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Upper bounds for GK-dimensions of finitely generated P.I. algebras


Author: Allan Berele
Journal: Proc. Amer. Math. Soc. 145 (2017), 1859-1864
MSC (2010): Primary 16P90; Secondary 16R99
DOI: https://doi.org/10.1090/proc/13456
Published electronically: November 21, 2016
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Abstract: We prove that if $ A$ is characteristic zero algebra generated by $ k$ elements and satisfying a polynomial identity of degree $ d$ then it has GK-dimension less than or equal to $ k\lfloor d/2\rfloor ^2$. We conjecture that the stronger upper bound that the GK-dimension of $ A$ is less than or equal to $ (k-1)\lfloor d/2\rfloor ^2 +1$ and prove it in a number of special cases.


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Additional Information

Allan Berele
Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614
Email: aberele@depaul.edu

DOI: https://doi.org/10.1090/proc/13456
Keywords: GK-dimension, polynomial identity, cocharacter sequence
Received by editor(s): May 22, 2015
Received by editor(s) in revised form: June 21, 2016
Published electronically: November 21, 2016
Communicated by: Harm Derksen
Article copyright: © Copyright 2016 American Mathematical Society

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