  The Temperley-Lieb and Brauer algebras and their cyclotomic analogues, as
well as the partition algebra, are all examples of twisted semigroup algebras.
We prove a general theorem about the cellularity of twisted semigroup algebras
of regular semigroups. This theorem, which generalises a recent result of East
about semigroup algebras of inverse semigroups, allows us to easily reproduce
the cellularity of these algebras.
