Automorphisms and coordinates of polynomial algebras (Q2704367)

For the most part, this is a paper which surveys the topic of \(R\)-automorphisms of \(R[x,y]\), where \(R\) is a commutative domain containing the rational numbers, and \(R[x,y]\) is a polynomial ring in 2 variables over \(R\). Of special interest is the case when \(R\) itself is a polynomial ring over a field. Emphasis is given to two particular topics: NEWLINENEWLINENEWLINE(1) Questions of tameness and stable tameness of particular automorphisms; NEWLINENEWLINENEWLINE(2) Algorithms which use Gröbner bases, e.g., to decide whether an endomorphism is an automorphism, calculate inverses, or determine tameness over certain base rings. NEWLINENEWLINENEWLINEThe subject of group actions is largely excluded, but the authors give a detailed report of these two topics, including an extensive and up-to-date bibliography. NEWLINENEWLINENEWLINEOne correction to note: The correct reference for example 34 is number [29] in the authors' list, not [18] as stated.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00031].