Coordinates and Automorphisms of Polynomial and Free Associative Algebras of Rank Three
Abstract
We study zautomorphisms of the polynomial algebra K[x,y,z] and the free associative algebra K<x,y,z> over a field K, i.e., automorphisms which fix the variable z. We survey some recent results on such automorphisms and on the corresponding coordinates. For K<x,y,z> we include also results about the structure of the ztame automorphisms and algorithms which recognize ztame automorphisms and ztame coordinates.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606304
 Bibcode:
 2006math......6304D
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Commutative Algebra;
 Primary 16S10. Secondary 16W20;
 16Z05;
 13B10;
 13B25;
 14E07