Graded cellular bases for TemperleyLieb algebras of type A and B
We show that the TemperleyLieb algebra of type A and the blob algebra (also known as the TemperleyLieb algebra of typeB) 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.
temperleylieb algebra khovanovlaudarouquier algebra cellular basis decomposition numbers