  Twisted Calabi-Yau algebras are a generalisation of Ginzburg's notion of
Calabi-Yau algebras. Such algebras A come equipped with a modular automorphism
\sigma \in Aut(A), the case \sigma = id being precisely the original class of
Calabi-Yau algebras. Here we prove that every twisted Calabi-Yau algebra may be
extended to a Calabi-Yau algebra. More precisely, we show that if A is a
twisted Calabi-Yau algebra with modular automorphism \sigma, then the smash
product algebras A \rtimes_\sigma N and A \rtimes_\sigma Z are Calabi-Yau.
