Pascal's triangle and word bases for blob algebra ideals
P P Martin
TL;DR
This paper provides an elementary proof demonstrating the isomorphism between the blob algebra and the extended Temperley-Lieb algebra, highlighting their structural equivalence through diagrammatic and presentation-based approaches.
Contribution
It offers a new, straightforward proof of the algebraic isomorphism, clarifying the relationship between blob and Temperley-Lieb algebras.
Findings
Established the isomorphism between blob and extended Temperley-Lieb algebras
Provided an elementary, presentation-based proof of the isomorphism
Clarified the algebraic and diagrammatic correspondence
Abstract
We give an elementary proof of isomorphism of the blob (diagram) algebra and the corresponding extended Temperley-Lieb algebra (defined by presentation).
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Polynomial and algebraic computation