  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.

Representation Theory;Quantum Algebra