Upper bounds for GK-dimensions of finitely generated P.I. algebras
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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.References
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Additional Information
- Allan Berele
- Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614
- Email: aberele@depaul.edu
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1859-1864
- MSC (2010): Primary 16P90; Secondary 16R99
- DOI: https://doi.org/10.1090/proc/13456
- MathSciNet review: 3611302