2010/10/16 by Tetiana Budnitska, Budnitska, Tetiana, Nadiya Budnitska +1
Mathematics · #15A21 #37C15 #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Representation Theory (math.RT) #math.DS #math.GN #math.RT #msc:15A21 #msc:37C15
paper · pdf · doi:10.48550/arxiv.1010.3381
arxiv created 2010/10/16 · arxiv updated 2010/10/19
Let f(x)=Ax+b and g(x)=Cx+d be two affine operators given by n-by-n matrices A and C and vectors b and d over a field F. They are said to be biregularly conjugate if hf=gh for some bijection h: Fn-->Fn being biregular, this means that the coordinate functions of h and h-1 are polynomials. Over an algebraically closed field of characteristic 0, we obtain necessary and sufficient conditions of biregular conjugacy of affine operators and give a canonical form of an affine operator up to biregular conjugacy. These results for bijective affine operators were obtained by J.Blanc [Conjugacy classes of affine automorphisms of Kn and linear automorphisms of Pn in the Cremona groups, Manuscripta Math. 119 (2006) 225-241].