Even Temperley-Lieb algebras and the dga of planar loops
Rachael Boyd, Guy Boyde, Oscar Randal-Williams, Robin J. Sroka
TL;DR
This paper demonstrates that the homology of even-stranded Temperley-Lieb algebras is governed by a differential graded algebra of planar loops, revealing complex algebraic structures and providing a simplified model for analysis.
Contribution
It introduces a differential graded algebra model for the homology of even-stranded Temperley-Lieb algebras, offering new insights into their algebraic structure.
Findings
Homology of even-stranded Temperley-Lieb algebra is highly nontrivial.
Homology is governed by a differential graded algebra of planar loops.
A small model for this differential graded algebra is constructed.
Abstract
We show that the homology of a Temperley-Lieb algebra on an even number of strands has a rich algebraic structure and is highly nontrivial in general. This is achieved by proving that it is entirely governed by a differential graded algebra: the differential graded algebra of planar loops. We provide a small model for this dga, and use it to obtain consequences on homology.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models