Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Request Permissions   Purchase Content 
 

 

The implicit function theorem and free algebraic sets


Authors: Jim Agler and John E. M$^{\mathrm{c}}$Carthy
Journal: Trans. Amer. Math. Soc. 368 (2016), 3157-3175
MSC (2010): Primary 14M99, 16S50
DOI: https://doi.org/10.1090/tran/6546
Published electronically: July 22, 2015
MathSciNet review: 3451873
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove an implicit function theorem for non-commutative functions. We use this to show that if $ p(X,Y)$ is a generic non-commuting polynomial in two variables and $ X$ is a generic matrix, then all solutions $ Y$ of $ p(X,Y)=0$ will commute with $ X$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 14M99, 16S50

Retrieve articles in all journals with MSC (2010): 14M99, 16S50


Additional Information

Jim Agler
Affiliation: Department of Mathematics, University of California San Diego, La Jolla, California 92093

John E. M$^{\mathrm{c}}$Carthy
Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130

DOI: https://doi.org/10.1090/tran/6546
Keywords: NC functions, free holomorphic functions, free algebraic sets
Received by editor(s): February 19, 2014
Published electronically: July 22, 2015
Additional Notes: The first author was partially supported by National Science Foundation Grant DMS 1068830
The second author was partially supported by National Science Foundation Grant DMS 1300280
Article copyright: © Copyright 2015 American Mathematical Society