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Algebraic Geometry Commons

Open Access. Powered by Scholars. Published by Universities.®

2016

NC functions

Articles 1 - 2 of 2

Full-Text Articles in Algebraic Geometry

Non-Commutative Automorphisms Of Bounded Non-Commutative Domains, John E. Mccarthy, Richard M. Timoney Oct 2016

Non-Commutative Automorphisms Of Bounded Non-Commutative Domains, John E. Mccarthy, Richard M. Timoney

Mathematics Faculty Publications

We establish rigidity (or uniqueness) theorems for non-commutative (NC) automorphisms that are natural extensions of classical results of H. Cartan and are improvements of recent results. We apply our results to NC domains consisting of unit balls of rectangular matrices.


The Implicit Function Theorem And Free Algebraic Sets, Jim Agler, John E. Mccarthy May 2016

The Implicit Function Theorem And Free Algebraic Sets, Jim Agler, John E. Mccarthy

Mathematics Faculty Publications

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