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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title = "Limits of traces of Temperley-Lieb algebras",

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.",

keywords = "Diagrammatic algebra, Non-semisimple algebra, Temperley-Lieb algebra",

author = "Moore, \{Stephen T.\}",

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year = "2024",

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doi = "10.1016/j.jalgebra.2023.12.018",

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AU - Moore, Stephen T.

PY - 2024/3/15

Y1 - 2024/3/15

N2 - 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.

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.

KW - Diagrammatic algebra

KW - Non-semisimple algebra

KW - Temperley-Lieb algebra

UR - https://www.scopus.com/pages/publications/85181150470

U2 - 10.1016/j.jalgebra.2023.12.018

DO - 10.1016/j.jalgebra.2023.12.018

M3 - Article

AN - SCOPUS:85181150470

SN - 0021-8693

VL - 642

SP - 95

EP - 147

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Limits of traces of Temperley-Lieb algebras

Abstract

Keywords

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