Limits of traces of Temperley-Lieb algebras

Stephen T. Moore

doi:10.1016/j.jalgebra.2023.12.018

Limits of traces of Temperley-Lieb algebras

Stephen T. Moore

University of Wroc-law

Research output: Contribution to journal › Article › peer-review

Abstract

We review the classification of positive extremal traces on the generic infinite Temperley-Lieb algebra, and then extend the classification to the non-semisimple root of unity case. As a result, we obtain Hilbert space structures on the full infinite Temperley-Lieb algebra at roots of unity.

Original language	English
Pages (from-to)	95-147
Number of pages	53
Journal	Journal of Algebra
Volume	642
DOIs	https://doi.org/10.1016/j.jalgebra.2023.12.018
Publication status	Published - 15 Mar 2024
Externally published	Yes

Keywords

Diagrammatic algebra
Non-semisimple algebra
Temperley-Lieb algebra

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10.1016/j.jalgebra.2023.12.018

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Moore, S. T. (2024). Limits of traces of Temperley-Lieb algebras. Journal of Algebra, 642, 95-147. https://doi.org/10.1016/j.jalgebra.2023.12.018

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AB - We review the classification of positive extremal traces on the generic infinite Temperley-Lieb algebra, and then extend the classification to the non-semisimple root of unity case. As a result, we obtain Hilbert space structures on the full infinite Temperley-Lieb algebra at roots of unity.

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Limits of traces of Temperley-Lieb algebras

Abstract

Keywords

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