منابع مشابه
The Jacobian Conjecture Is Stably Equivalent to the Dixmier Conjecture
The paper is devoted to the proof of equivalence of Jacobian and Dixmier conjectures. We show that 2n-dimensional Jacobian conjecture implies Dixmier conjecture for Wn. The proof uses “antiquantization”: positive characteristics and Poisson brackets on the center of Weyl algebra in characteristic p. 2000 Math. Subj. Class. 16S32, 16S80, 14R15.
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In 1958 Lax conjectured that hyperbolic polynomials in three variables are determinants of linear combinations of three symmetric matrices. This conjecture is equivalent to a recent observation of Helton and Vinnikov. Consider a polynomial p on R of degree d (the maximum of the degrees of the monomials in the expansion of p). We call p homogeneous if p(tw) = tp(w) for all real t and vectors w ∈...
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In 1977 a five-part conjecturewasmade about a family of groups related to trivalent graphs and one part of the conjecture was proved. The conjecture completely determines all finite members of the family. Here we prove another part of the conjecture and foreshadow a paper which completes the proof of the other three parts.
متن کاملToida's Conjecture is True
Let S be a subset of the units in Zn. Let Γ be a circulant graph of order n (a Cayley graph of Zn) such that if ij ∈ E(Γ), then i − j (mod n) ∈ S. Toida conjectured that if Γ′ is another circulant graph of order n, then Γ and Γ′ are isomorphic if and only if they are isomorphic by a group automorphism of Zn. In this paper, we prove that Toida’s conjecture is true. We further prove that Toida’s ...
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The Jacobian Conjecture can be generalized and is established : Let S be a polynomial ring over a field of characteristic zero in finitely may variables. Let T be an unramified, finitely generated extension of S with T = k . Then T = S. Let k be an algebraically closed field, let k be an affine space of dimension n over k and let f : k −→ k be a morphism of algebraic varieties. Then f is given ...
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ژورنال
عنوان ژورنال: SSRN Electronic Journal
سال: 2017
ISSN: 1556-5068
DOI: 10.2139/ssrn.2964456