Graded cellular bases for Temperley-Lieb algebras of type A and B

David Plaza; Steen Ryom-Hansen

Graded cellular bases for Temperley-Lieb algebras of type A and B

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arxiv 1203.2592 v3 pith:FBGX6QCK submitted 2012-03-12 math.RT math.QA

David Plaza , Steen Ryom-Hansen This is my paper · ORCID

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keywords algebrasgradedalgebramodulestemperley-liebtypecellularbases

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abstract

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.

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