Cellularity of Diagram Algebras as Twisted Semigroup Algebras

@inproceedings{Wilcox2005CellularityOD,
  title={Cellularity of Diagram Algebras as Twisted Semigroup Algebras},
  author={S. Wilcox},
  year={2005}
}
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. 

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