Affine structures on abelian Lie Groups
نویسنده
چکیده
The Nagano-Yagi-Goldmann theorem states that on the torus T, every affine (or projective) structure is invariant or is constructed on the basis of some Goldmann rings [N-Y]. It shows the interest to study the invariant affine structure on the torus T or on abelian Lie groups. Recently, the works of Kim [K] and Dekempe-Ongenae [D-O] precise the number of non equivalent invariant affine structure on a abelian Lie group in the case where these structures are complete. In this paper we propose a study of complete and non complete affine structure on abelian Lie groups based on the geometry of the algebraic variety of finite dimensional associative algebras.
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