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Let k be an algebraically closed field. Given an extension A : B offinite-dimensional k- algebras, we establish criteria ensuring that therepresentation-theoretic notion of polynomial growth is preserved under ascentand descent. These results are then used to show that principal blocks offinite group schemes of odd characteristic are of polynomial growth if and onlyif they are Morita equivalent to trivial extensions of radical square zero tamehereditary algebras. In that case, the blocks are of domestic representationtype and the underlying group schemes are closely related to binary polyhedralgroup schemes.

Extensions of tame algebras and finite group schemes of domestic representation type