Finite-dimensional differential algebraic groups and the Picard-Vessiot theory

• Autorzy: Anand Pillay
• Języki publikacji: EN

Abstrakty

EN

We make some observations relating the theory of finite-dimensional differential algebraic groups (the ∂₀-groups of [2]) to the Galois theory of linear differential equations. Given a differential field (K,∂), we exhibit a surjective functor from (absolutely) split (in the sense of Buium) ∂₀-groups G over K to Picard-Vessiot extensions L of K, such that G is K-split iff L = K. In fact we give a generalization to "K-good" ∂₀-groups. We also point out that the "Katz group" (a certain linear algebraic group over K) associated to the linear differential equation ∂Y = AY over K, when equipped with its natural connection ∂ - [A,-], is K-split just if it is commutative.

Kategorie tematyczne

• 34M60: Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent)
• 12H05: Differential algebra

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2002
• Tom: 58
• Numer: 1
• Strony: 189-199

Daty

wydano

2002

Twórcy

autor

Anand Pillay

• Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green St., Urbana, IL 61801, U.S.A.
• Institut für Mathematik, Humboldt Universität, D-10099 Berlin, Germany

Identyfikatory

DOI

10.4064/bc58-0-14