Central polynomials of associative algebras and their growth
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- by Antonio Giambruno and Mikhail Zaicev PDF
- Proc. Amer. Math. Soc. 147 (2019), 909-919 Request permission
Abstract:
A central polynomial for an algebra $A$ is a polynomials in noncommutative variables taking central values in $A$. If an algebra has central polynomials, e.g., the algebra of $k\times k$ matrices, can one measure how many are there?
Here we study the growth of central polynomials for any algebra satisfying a polynomial identity over a field of characteristic zero. We prove the existence of two limits called the central exponent and the proper central exponent of $A$. They give a measure of the exponential growth of the central polynomials and the proper central polynomials of $A$. They are comparable with $exp(A)$, the PI-exponent of the algebra.
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Additional Information
- Antonio Giambruno
- Affiliation: Dipartimento di Matematica e Informatica, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy
- MR Author ID: 73185
- ORCID: 0000-0002-3422-2539
- Email: antonio.giambruno@unipa.it, antoniogiambr@gmail.com
- Mikhail Zaicev
- Affiliation: Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119992 Russia
- MR Author ID: 256798
- Email: zaicevmv@mail.ru
- Received by editor(s): January 1, 2018
- Published electronically: December 3, 2018
- Additional Notes: The first author was partially supported by the GNSAGA of INDAM. The second author was supported by the Russian Science Foundation, grant 16-11-10013
- Communicated by: Jerzy Weyman
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 909-919
- MSC (2010): Primary 16R10, 16R99; Secondary 16P90
- DOI: https://doi.org/10.1090/proc/14172
- MathSciNet review: 3896042