Cellularity of diagram algebras as twisted semigroup algebras

By Stewart Wilcox. 2007

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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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3ee7bfb2a19a55133f4aec43fddfd9f8d0898d64