  Consider an automorphism group of a finite-dimensional algebra. S. Halperin
conjectured that the unity component of this group is solvable if the algebra
is a complete intersection. The solvability criterion recently obtained by M.
Schulze provides a proof to a local case of this conjecture as well as gives an
alternative proof of S.S.--T. Yau's theorem based on a powerful result due to
G. Kempf. In this note we finish the proof of Halperin's conjecture and study
the extremal cases in Schulze's criterion, where the algebra of derivations is
non-solvable. This allows us to reduce a direct, self-contained proof of Yau's
theorem.
