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Idempotents in the Temperley-Lieb Monoid and Other Categories

  • Louis H Kauffman
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Abstract

This paper examines idempotents in algebras and categories that arise from factorizations of the identity morphism. In the diagrammatic and combinatorial contexts considered here, these factorizations correspond to generalizations of meanders, where a meander is understood to be a curve in the plane that wanders transversely back and forth across a given straight line. By formulating the algebra of the Temperley-Lieb Monoid in terms of planar curve combinatorics, one can understand idempotents in the Temperley-Lieb Monoid in terms of meanders. Corresponding results are shown for the Brauer Monoid and for the Tangle Monoid and Tangle Category.

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Cite

BibTeXRIS
BibTeX
@misc{kauffman2026idempotents,
  title = {{Idempotents in the Temperley-Lieb Monoid and Other Categories}},
  author = {Louis H Kauffman},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34282},
  eprint = {2609.34282},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34282},
}
RIS
TY  - UNPB
TI  - Idempotents in the Temperley-Lieb Monoid and Other Categories
AU  - Louis H Kauffman
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.34282
UR  - https://arxiv.org/abs/2609.34282
AB  - This paper examines idempotents in algebras and categories that arise from factorizations of the identity morphism. In the diagrammatic and combinatorial contexts considered here, these factorizations correspond to generalizations of meanders, where a meander is understood to be a curve in the plane that wanders transversely back and forth across a given straight line. By formulating the algebra of the Temperley-Lieb Monoid in terms of planar curve combinatorics, one can understand idempotents in the Temperley-Lieb Monoid in terms of meanders. Corresponding results are shown for the Brauer Monoid and for the Tangle Monoid and Tangle Category.
ER  -