Inversion of polynomial species and jacobian conjecture
نویسنده
چکیده
We consider the following problem in the theory of (virtual) species of structures: Given a polynomial species F such that its derivative dF equals 1, will its inverse w.r.t substitution F h?1i also be polynomial species? We shall see that this is in general not the case. From this result it follows that an analogue of the jacobian conjecture in the context of species does not hold.
منابع مشابه
Some Properties and Open Problems of Hessian Nilpotent Polynomials
In the recent progress [BE1], [M] and [Z2], the wellknown Jacobian conjecture ([BCW], [E]) has been reduced to a problem on HN (Hessian nilpotent) polynomials (the polynomials whose Hessian matrix are nilpotent) and their (deformed) inversion pairs. In this paper, we prove several results on HN polynomials, their (deformed) inversion pairs as well as the associated symmetric polynomial or forma...
متن کاملSome Properties of and Open Problems on Hessian Nilpotent Polynomials
In the recent work [BE1], [M], [Z1] and [Z2], the well-known Jacobian conjecture ([BCW], [E]) has been reduced to a problem on HN (Hessian nilpotent) polynomials (the polynomials whose Hessian matrix are nilpotent) and their (deformed) inversion pairs. In this paper, we prove several results on HN polynomials, their (deformed) inversion pairs as well as on the associated symmetric polynomial or...
متن کاملLegendre transform, Hessian conjecture and tree formula
Let φ be a polynomial over K (a field of characteristic 0) such that the Hessian of φ is a nonzero constant. Let φ̄ be the formal Legendre Transform of φ. Then φ̄ is well-defined as a formal power series over K. The Hessian Conjecture introduced here claims that φ̄ is actually a polynomial. This conjecture is shown to be true when K = R and the Hessian matrix of φ is either positive or negative de...
متن کاملThe inversion formula for automorphisms of the Weyl algebras and polynomial algebras
Let An be the n’th Weyl algebra and Pm be a polynomial algebra in m variables over a field K of characteristic zero. The following characterization of the algebras {An⊗Pm} is proved: an algebra A admits a finite set δ1, . . . , δs of commuting locally nilpotent derivations with generic kernels and ∩i=1ker(δi) = K iff A ≃ An ⊗ Pm for some n and m with 2n + m = s, and vice versa. The inversion fo...
متن کاملRecurrent Inversion Formulas
Let F (z) = z − H(z) with o(H(z)) ≥ 2 be a formal map from Cn to Cn and G(z) the formal inverse of F (z). In this paper, we give two recurrent formulas for the formal inverse G(z). The first formula not only provides an efficient method for the calculation of G(z), but also reduces the inversion problem to a Cauchy problem of a partial differential equation. The second one is differential free ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007