Submission date: 26 May 2010.

Abstract:

With any connected affine algebraic group G over an algebraically closed field K of characteristic zero, we associate another connected affine algebraic group D over K and a finite central subgroup F of D such that, up to isomorphism of algebraic groups, affine algebraic groups over K abstractly isomorphic to G are precisely the direct products of D/u(F) by s copies of the additive group K, where u is an abstract automorphism of D and s is an integer satisfying s=0 when the derived subgroup of G contains the identity component of the center of G.

The construction of D lies heavily on model theory and groups of finite Morley rank.

Mathematics Subject Classification: 03C60, 14L17, 20G15

Keywords and phrases: Affine algebraic groups, Abstract isomorphisms, Groups of finite Morley rank, Burdges' unipotence.

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