Classification of Quadratic Homogeneous Automorphisms in Dimension Five

REFERENCES

• Bass , H. , Connel , E. , Wright , D. ( 1982 ). The Jacobian conjecture: Reduction of degree and formal expansion of the inverse . Bull. Amer. Math. Soc. 7 ( 2 ): 287 – 330 .
   Web of Science ®Google Scholar
• de Bondt , M. ( 2006 ). Quasi-translations and counterexamples to the Homogeneous Dependence Problem . Proc. Amer. Math. Soc. 134 ( 10 ): 2849 – 2856 .
   Web of Science ®Google Scholar
• de Bondt , M. , van den Essen , A. ( 2005 ). A reduction of the Jacobian Conjecture to the symmetric case . Proc. Amer. Math. Soc. 133 ( 8 ): 2201 – 2205 .
   Web of Science ®Google Scholar
• de Bondt , M. , van den Essen , A. ( 2005 ). The Jacobian Conjecture: Linear triangularization for homogeneous polynomial maps in dimension three . J. Algebra 294 ( 1 ): 294 – 306 .
   Web of Science ®Google Scholar
• Drużkowski , L. M. ( 1983 ). An effective approach to the Jacobian Conjecture . Math. Ann. 264 ( 3 ): 303 – 313 .
   Web of Science ®Google Scholar
• van den Essen , A. ( 2000 ). Polynomial automorphisms and the Jacobian conjecture . Progress in Mathematics . Vol. 190 . Basel-Boston-Berlin : Birkhäuser .
   Google Scholar
• van den Essen , A. , Hubbers , E. ( 1996 ). Polynomial maps with strongly nilpotent Jacobian matrix and the Jacobian Conjecture . Linear Algebra Appl. 247 : 121 – 132 .
   Web of Science ®Google Scholar
• Fasoli , M. A. ( 1997 ). Classification of nilpotent linear spaces in M(4; ℂ) . Commun. Algebra 25 ( 6 ): 1919 – 1932 .
   Web of Science ®Google Scholar
• Freudenburg , G. ( 2006 ). Algebraic Theory of Locally Nilpotent Derivations . Berlin-Heidelbert-New York : Springer .
   Google Scholar
• Gurevich , G. B. ( 1964 ). Foundations of the theory of algebraic invariants . Groningen , The Netherlands : P. Noordhoff Ltd .
   Google Scholar
• Hubbers , E. ( 1994 ). Cubic similarity in dimension four. Master's Degree Thesis. The Netherlands: University of Nijmegen .
   Google Scholar
• Hubbers , E. ( 1998 ). Nilpotent Jacobians . Ph.D. thesis . The Netherlands : University of Nijmegen .
   Google Scholar
• Jacobson , N. ( 1962 ). Lie Algebras . New York : Interscience .
   Google Scholar
• Jung , H. ( 1942 ). Über ganze birationale Transformationen der Ebene . J. Reine. Angew. Math. 184 : 161 – 174 .
   Google Scholar
• van der Kulk , W. ( 1953 ). On polynomial rings in two variables . Nieuw Archiefvoor Wiskuncle 3 ( 1 ): 33 – 41 .
   Google Scholar
• Meisters , G. , Olech , C. ( 1991 ). Strong nilpotence holds in dimension up to five only . Linear Multilinear Algebra 30 ( 4 ): 231 – 255 .
   Google Scholar
• Rusek , K. Polynomial Automorphisms. Preprint 456, May 1989. IMPAN, Warsaw, Poland: Inst. of Math., Polish Acad. of Sciences .
   Google Scholar
• Shestakov , I. P. , Umirbaev , U. U. ( 2004 ). Poisson brackets and two-generated subalgebras of rings of polynomial . J. Amer. Math. Soc. 17 ( 1 ): 181 – 196 .
   Web of Science ®Google Scholar
• Shestakov , I. P. , Umirbaev , U. U. ( 2004 ). The tame and the wild automorphisms of polynomial rings in three variables . J. Amer. Math. Soc. 17 ( 1 ): 197 – 227 .
   Web of Science ®Google Scholar
• Wang , S. S. ( 1980 ). A Jacobian criterion for separability . J. Algebra 65 ( 2 ): 453 – 494 .
   Web of Science ®Google Scholar
• Wright , D. ( 1993 ). The Jacobian Conjecture: Linear triangularization for cubics in dimension three . Linear Multilinear Algebra 34 ( 2 ): 85 – 97 .
   Google Scholar
• Yu , J. T. ( 1995 ). On the Jacobian Conjecture: Reduction of coefficients . J. Algebra 171 ( 2 ): 515 – 523 .
   Web of Science ®Google Scholar
• Communicated by J.-T. Yu.
   Google Scholar