The tame and the wild automorphisms of polynomial rings in three variables
From MaRDI portal
Publication:4441815
DOI10.1090/S0894-0347-03-00440-5zbMath1056.14085OpenAlexW1675890124MaRDI QIDQ4441815
Ualbei Utmakhanbetovich Umirbaev, Ivan Pavlovic Shestakov
Publication date: 7 January 2004
Published in: Journal of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0894-0347-03-00440-5
Jacobian problem (14R15) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Computational aspects and applications of commutative rings (13P99) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (14R10)
Related Items
Weighted multidegrees of polynomial automorphisms over a domain, Tame and wild automorphisms of differential polynomial algebras of rank 2, Identities in group rings, enveloping algebras and Poisson algebras, On the tame automorphisms of differential polynomial algebras, Automorphisms and derivations of \(U_q(\mathfrak{sl}^+_4)\), On the automorphisms of quantum Weyl algebras, Almost Tame Automorphisms of Two Generated Free Leibniz Algebras, A survey on Zariski cancellation problem, The automorphism groups for a family of generalized Weyl algebras, Free Poisson fields and their automorphisms, Defining relations for automorphism groups of free algebras, On tameness of Matsumoto-Imai central maps in three variables over the finite field \(\mathbb F_2\), Primitive ideals and automorphisms of quantum matrices., The prime spectrum and simple modules over the quantum spatial ageing algebra, Automorphisms and derivations of free Poisson algebras in two variables, Dynamics of polynomial diffeomorphisms of \(\mathbb {C}^2\): combinatorial and topological aspects, Lie structure of truncated symmetric Poisson algebras, Diffeomorphisms preserving symplectic data on submanifolds, Quadratic tame generators problem of rank three, Normal subgroups generated by a single polynomial automorphism, Poisson structures on finitary incidence algebras, The affine automorphism group of \(\mathbb{A}^{3}\) is not a maximal subgroup of the tame automorphism group, The Jacobian Conjecture, Together with Specht and Burnside-Type Problems, How to Prove the Wildness of Polynomial Automorphisms: An Example, Strongly Residual Coordinates over A[x], Keller Maps of Low Degree over Finite Fields, Igor Rostislavovich Shafarevich and his mathematical heritage, Linearized polynomial maps over finite fields, The discriminant criterion and automorphism groups of quantized algebras., The local structure of groups of triangular automorphisms of relatively free algebras., On the automorphisms of a free Lie algebra of rank 3 over an integral domain, Multidegrees of tame automorphisms in dimension three, Nonabelian 1-cohomologies and conjugacy of finite subgroups in some extensions., A parachute for the degree of a polynomial in algebraically independent ones, Groups of triangular automorphisms of a free associative algebra and a polynomial algebra., Masayoshi Nagata (1927-2008) and his mathematics, Some properties of the group of birational maps generated by the automorphisms of \(\mathbb P^n_{\mathbb C}\) and the standard involution, Endomorphisms of polynomial algebras with small co-invariants, Degree estimate for subalgebras generated by two elements., Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields, Stably co-tame polynomial automorphisms over commutative rings, The tame and the wild automorphisms of an affine quadric threefold, Flexible varieties and automorphism groups, Separability of wild automorphisms of a polynomial ring, Stable tameness of two-dimensional polynomial automorphisms over a regular ring, Periodic automorphisms of the free Lie algebra of rank 3, Coordinates and automorphisms of polynomial and free associative algebras of rank three., Algebras of Jordan brackets and generalized Poisson algebras, On multidegrees of tame and wild automorphisms of \(\mathbb C^3\), Quadratic linear Keller maps of nilpotency index three, On the lifting of the Nagata automorphism, Rigidity of quantum tori and the Andruskiewitsch-Dumas conjecture, Maps that are roots of power series, A generalization of the Shestakov-Umirbaev inequality, The discriminant controls automorphism groups of noncommutative algebras., Triangulable locally nilpotent derivations in dimension three, Locally tame plane polynomial automorphisms, On the work of Sarig on countable Markov chains and thermodynamic formalism, On the Karaś type theorems for the multidegrees of polynomial automorphisms, Jet groups, The isomorphism problem for multiparameter quantized Weyl algebras., Closed subgroups of the polynomial automorphism group containing the affine subgroup, Automorphisms of ideals of polynomial rings, Bipartite algebraic graphs without quadrilaterals, Discriminants and automorphism groups of Veronese subrings of skew polynomial rings, Kirwan surjectivity for quiver varieties, Degree growth of polynomial automorphisms and birational maps: some examples, A presentation of a finitely generated submonoid of invertible endomorphisms of the free monoid, The Nagata automorphism of free nonassociative algebras of rank two over Euclidean domains, On commuting polynomial automorphisms of \({\mathbb{C}}^{k}\), \(k \geq 3\), Test elements, retracts and automorphic orbits., Fractal nil graded Lie, associative, Poisson, and Jordan superalgebras, The strong Anick conjecture is true., When is a polynomial ideal binomial after an ambient automorphism?, Power linear Keller maps of rank two are linearly triangularizable, Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism, On quadratic homogeneous quasi-translations, Automorphisms of finitely generated relatively free bicommutative algebras, Tame automorphisms of \(\mathbb C^3\) with multidegree of the form \((3,d_{2},d_{3})\), Locally nilpotent derivations of free algebra of rank two, Locally finite polynomial endomorphisms, Relations between the leading terms of a polynomial automorphism, Commutator automorphisms of formal power series rings, A note on \(k[z\)-automorphisms in two variables], Degeneration of Tame Automorphisms of a Polynomial Ring, ON GENERATORS OF THE TAME INVERTIBLE POLYNOMIAL MAPS GROUP, The Nagata automorphism is shifted linearizable, The automorphisms group and the classification of gradings of finite dimensional associative algebras, There is no tame automorphism of $\mathbb{C}^{3}$ with multidegree $(3,4,5)$, Remarks on a Normal Subgroup ofGAn, Automorphisms of a polynomial ring which admit reductions of type I, A retrospect of the research in nonassociative algebras in IME-USP, Generalization of an Invertible Transformation and Examples of its Applications, Degree estimate for commutators., Automorphisms fixing a variable of \(K\langle x,y,z\rangle\)., Generalisations of the tame automorphisms over a domain of positive characteristic, The generalized amalgamated product structure of the tame automorphism group in dimension three, Automorphisms of the Weyl algebra., The profinite polynomial automorphism group, The Nagata Type Polynomial Automorphisms and Rectifiable Space Lines, The Anick automorphism of free associative algebras, A new class of finitely generated polynomial subalgebras without finite SAGBI bases, Cryptographic Technology for Benefiting from Big Data, О тождествах специального вида в алгебрах Лейбница - Пуассона, Automorphisms of the endomorphism semigroup of a free algebra, Dependence between homogeneous components of polynomials with small degree of Poisson bracket, Automorphisms of the affine 3-space of degree 3, Free generic Poisson fields and algebras, Lifting of polynomial symplectomorphisms and deformation quantization, CLASSIFICATION OF CUBIC HOMOGENEOUS POLYNOMIAL MAPS WITH JACOBIAN MATRICES OF RANK TWO, Gradings allowing wild automorphisms, Automorphisms of affine Veronese surfaces, Tame automorphism groups of polynomial rings with property (T) and infinitely many alternating group quotients, Linearity and nonlinearity of groups of polynomial automorphisms of the plane, Scale for codimension growth of Poisson PI-algebras, Automorphisms of simple quotients of the Poisson and universal enveloping algebras of sl2, Transposed Poisson structures, Graded automorphisms of the algebra of polynomials in three variables, A unified approach to embeddings of a line in 3-space, Centers and automorphisms of PI quantum matrix algebras, ON THE AUTOMORPHISM GROUP OF A FREE METABELIAN LIE ALGEBRA, THE FREIHEITSSATZ AND THE AUTOMORPHISMS OF FREE RIGHT-SYMMETRIC ALGEBRAS, On the augmentation topology of automorphism groups of affine spaces and algebras, Unnamed Item, The Strong Anick Conjecture, TAME AUTOMORPHISMS FIXING A VARIABLE OF FREE ASSOCIATIVE ALGEBRAS OF RANK THREE, On the Strong Nilpotence Problem, Rigidity of Quadratic Poisson Tori, Today’s menu: Geometry and resolution of singular algebraic surfaces, Classification of Quadratic Homogeneous Automorphisms in Dimension Five, Linearly triangularizable quadratic endomorphisms, Combinatorics of the tame automorphism group, Unnamed Item, The group of Cremona transformations generated by linear maps and the standard involution, The strong Nagata conjecture, Constant weighted sums of iterates, Co-tame polynomial automorphisms, Automorphisms of ore extensions by skew derivations, Algebraic hypersurfaces, Ualbai Utmakhanbetovich Umirbaev, On Generators of the Tame Automorphism Group of Free Metabelian Lie Algebras, Centralizers in free Poisson algebras, Defining relations of the tame automorphism group of polynomial algebras in three variables, Some co-tame automorphisms of affine spaces, Automorphism group of green algebra of weak Hopf algebra corresponding to Sweedler Hopf algebra, Symmetric polynomials in the free metabelian Poisson algebras
Cites Work
- Stably tame automorphisms
- A non-triangular action of \({\mathbb{G}}_ a\) on \({\mathbb{A}}^ 3\)
- Quantization of Poisson superalgebras and speciality of Jordan Poisson superalgebras
- Polynomial automorphisms and the Jacobian conjecture
- Using Gröbner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence
- AUTOMORPHISMS OF TWO-GENERATED FREE LEIBNIZ ALGEBRAS
- Poisson brackets and two-generated subalgebras of rings of polynomials
- Tame and Wild Coordinates of 𝐾[𝑧[𝑥,𝑦]]
- Automorphisms of a Free Associative Algebra of Rank 2.I
- Über ganze birationale Transformationen der Ebene.
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item