A pr 2 00 1 ON A GENERIC INVERSE DIFFERENTIAL GALOIS PROBLEM FOR GL
نویسنده
چکیده
In this paper we construct a generic Picard-Vessiot extension for the general linear groups. In the case when the differential base field has finite transcen-dence degree over its field of constants we provide necessary and sufficient conditions for solving the inverse differential Galois problem for this groups via specialization from our generic extension.
منابع مشابه
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We give sufficient conditions for a differential equation to have a given semisimple group as its Galois group. For any group G with G0 = G1 · . . . · Gr where each Gi is a simple group of type Al, Cl, Dl, E6 or E7, we construct a differential equation over C(x) having Galois group G.
متن کاملPRINCIPAL DIFFERENTIAL IDEALS AND A GENERIC INVERSE DIFFERENTIAL GALOIS PROBLEM FOR GLn
We characterize the principal differential ideals of a polynomial ring in n indeterminates with coefficients in the ring of differential polynomials in n indeterminates and derivation given by a “general” element of Lie(GLn) and use this characterization to construct a generic Picard-Vessiot extension for GLn. In the case when the differential base field has finite transcendence degree over its...
متن کامل0 on a Generic Inverse Differential Galois Problem
Let F be a differential field with algebraically closed field of constants C.
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تاریخ انتشار 2001