Principal bundles, quasi-abelian varieties and structure of algebraic groups

Abstract: We classify principal bundles over anti-affine schemes with affine and commutative structure group. We show that this yields the classification of quasi-abelian varieties over a field k (i.e., group k-schemes G such that ). The interest of this result is given by the fact that the classification of smooth group k-schemes is reduced to the classification of quasi-abelian varieties and of certain affine group schemes. [Copyright &y& Elsevier]