TL;DR
This paper introduces a new, conceptually simple proof of the Temperley-Lieb algebra's presentation using twisted semigroup algebras and novel submonoids, offering fresh insights into its algebraic structure.
Contribution
It provides an alternative, straightforward proof of the Temperley-Lieb algebra's presentation, utilizing twisted semigroup algebras and identifying new submonoids.
Findings
New proof of Temperley-Lieb algebra presentation
Introduction of two new submonoids of the Temperley-Lieb monoid
Application of twisted semigroup algebras
Abstract
We give a new and conceptually straightforward proof of the well-known presentation for the Temperley-Lieb algebra, via an alternative new presentation. Our method involves twisted semigroup algebras, and we make use of two apparently new submonoids of the Temperley-Lieb monoid.
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