Graded cellular bases for Temperley-Lieb algebras of type A and B
  We show that the Temperley-Lieb algebra of type $A$ and the blob algebra (also known as the Temperley-Lieb algebra of type $ B$) at roots of unity are $ \mathbb Z$-graded algebras.We moreover show that they are graded cellular algebras, thus making their cell modules, or standard modules, graded modules for the algebras. 
David Plaza, Steen Ryom-Hansen
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