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521
Polynomial Automorphisms and the Jacobian Conjecture
 OF IN PROGRESS IN MATHEMATICS, BIRKHÄUSER
, 2000
"... In this paper we give an update survey of the most important results concerning the Jacobian conjecture: several equivalent descriptions are given and various related conjectures are discussed. At the end of the paper, we discuss the recent counterexamples, in all dimensions greater than two, to th ..."
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Cited by 145 (5 self)
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In this paper we give an update survey of the most important results concerning the Jacobian conjecture: several equivalent descriptions are given and various related conjectures are discussed. At the end of the paper, we discuss the recent counterexamples, in all dimensions greater than two, to the MarkusYamabe conjecture (Global asymptotic Jacobian conjecture).
On the polynomial automorphisms of a group
 Acta Sci. Math. (Szeged
"... Abstract. Let A(G) denote the automorphism group of a group G. A polynomial automorphism of G is an automorphism of the form x ↦ → (v −1 1 xǫ1 v1)...(v −1 m xǫm vm). We prove that if G is nilpotent (resp. metabelian), then so is the subgroup of A(G) generated by all polynomial automorphisms. 1. Intr ..."
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Cited by 1 (1 self)
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Abstract. Let A(G) denote the automorphism group of a group G. A polynomial automorphism of G is an automorphism of the form x ↦ → (v −1 1 xǫ1 v1)...(v −1 m xǫm vm). We prove that if G is nilpotent (resp. metabelian), then so is the subgroup of A(G) generated by all polynomial automorphisms. 1
LENGTH FOUR POLYNOMIAL AUTOMORPHISMS
, 2008
"... We study the structure of length four polynomial automorphisms of R[X, Y] when R is a UFD. The results from this study are used to prove that if SLm(R[X1, X2,..., Xn]) = Em(R[X1, X2,..., Xn]) for all n, m ≥ 0 then all length four polynomial automorphisms of R[X, Y] that are conjugates are stably t ..."
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We study the structure of length four polynomial automorphisms of R[X, Y] when R is a UFD. The results from this study are used to prove that if SLm(R[X1, X2,..., Xn]) = Em(R[X1, X2,..., Xn]) for all n, m ≥ 0 then all length four polynomial automorphisms of R[X, Y] that are conjugates are stably
On reconstruction of polynomial automorphisms
, 1996
"... We extend results on reconstructing a polynomial automorphism from its restriction to the coordinate hyperplanes to some wider class of algebraic surfaces. We show that the algorithm proposed by M. Kwieciński in [K2] and based on Gröbner bases works also for this class of surfaces. ..."
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We extend results on reconstructing a polynomial automorphism from its restriction to the coordinate hyperplanes to some wider class of algebraic surfaces. We show that the algorithm proposed by M. Kwieciński in [K2] and based on Gröbner bases works also for this class of surfaces.
SOME STABLY TAME POLYNOMIAL AUTOMORPHISMS
, 2008
"... We study the structure of length three polynomial automorphisms of R[X, Y] when R is a UFD. These results are used to prove that if SLm(R[X1, X2,..., Xn]) = Em(R[X1, X2,..., Xn]) for all n, ≥ 0 and for all m≥3 then all length three polynomial automorphisms of R[X, Y] are stably tame. ..."
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Cited by 1 (1 self)
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We study the structure of length three polynomial automorphisms of R[X, Y] when R is a UFD. These results are used to prove that if SLm(R[X1, X2,..., Xn]) = Em(R[X1, X2,..., Xn]) for all n, ≥ 0 and for all m≥3 then all length three polynomial automorphisms of R[X, Y] are stably tame.
Reversors and symmetries for polynomial automorphisms of the plane
, 2003
"... We obtain normal forms for symmetric and for reversible polynomial automorphisms (polynomial maps that have polynomial inverses) of the plane. Our normal forms are based on the generalized Hénon normal form of Friedland and Milnor. We restrict to the case that the symmetries and reversors are also ..."
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Cited by 12 (3 self)
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We obtain normal forms for symmetric and for reversible polynomial automorphisms (polynomial maps that have polynomial inverses) of the plane. Our normal forms are based on the generalized Hénon normal form of Friedland and Milnor. We restrict to the case that the symmetries and reversors
Polynomial automorphisms and invariants
 J. Algebra
"... The version of the following full text has not yet been defined or was untraceable and may differ from the publisher's version. For additional information about this publication click this link. ..."
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Cited by 3 (0 self)
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The version of the following full text has not yet been defined or was untraceable and may differ from the publisher's version. For additional information about this publication click this link.
On Polynomial Automorphisms of Affine Spaces
, 2000
"... Some general results on algebraic group actions, with a focus on linearizability, are obtained. They are applied to proving that any faithful algebraic action of a connected reductive algebraic group G on ndimensional ane space A n over an algebraically closed field of characteristic zero is linear ..."
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Some general results on algebraic group actions, with a focus on linearizability, are obtained. They are applied to proving that any faithful algebraic action of a connected reductive algebraic group G on ndimensional ane space A n over an algebraically closed field of characteristic zero is linearizable in either of the cases: (1) n= 3; (2) n=4 and G is not a one or two dimensional torus.
Results 1  10
of
521