Coordinates and Automorphisms of Polynomial and Free Associative Algebras of Rank Three
Abstract
We study z-automorphisms 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 z-tame automorphisms and algorithms which recognize z-tame automorphisms and z-tame coordinates.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- June 2006
- DOI:
- 10.48550/arXiv.math/0606304
- arXiv:
- arXiv:math/0606304
- Bibcode:
- 2006math......6304D
- Keywords:
-
- Mathematics - Rings and Algebras;
- Mathematics - Commutative Algebra;
- Primary 16S10. Secondary 16W20;
- 16Z05;
- 13B10;
- 13B25;
- 14E07