Standard

Projectors in the virtual Temperley–Lieb algebra. / Deng, Qingying; Jin, Xian’an; Kauffman, Louis h.

In: Journal of Knot Theory and its Ramifications, Vol. 34, No. 5, 2550020, 2025.

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

Harvard

Deng, Q, Jin, X & Kauffman, LH 2025, 'Projectors in the virtual Temperley–Lieb algebra', Journal of Knot Theory and its Ramifications, vol. 34, no. 5, 2550020. https://doi.org/10.1142/S0218216525500208

APA

Deng, Q., Jin, X., & Kauffman, L. H. (2025). Projectors in the virtual Temperley–Lieb algebra. Journal of Knot Theory and its Ramifications, 34(5), [2550020]. https://doi.org/10.1142/S0218216525500208

Vancouver

Deng Q, Jin X, Kauffman LH. Projectors in the virtual Temperley–Lieb algebra. Journal of Knot Theory and its Ramifications. 2025;34(5):2550020. doi: 10.1142/S0218216525500208

Author

Deng, Qingying ; Jin, Xian’an ; Kauffman, Louis h. / Projectors in the virtual Temperley–Lieb algebra. In: Journal of Knot Theory and its Ramifications. 2025 ; Vol. 34, No. 5.

BibTeX

@article{89f05b4155ed4c309acb20542f640584,
title = "Projectors in the virtual Temperley–Lieb algebra",
abstract = "In this paper, we present a method of defining projectors in the virtual Temperley-Lieb algebra, that generalizes the Jones-Wenzl projectors in Temperley-Lieb algebra. We show that the projectors have similar properties with the Jones-Wenzl projectors, and contain an extra property which is associated with the virtual generator elements, that is, the product of a projector with a virtual generator is unchanged. We also show the uniqueness of the projector fn in terms of its axiomatic properties in the virtual Temperley-Lieba algebra VTLn(d). Finally, we find the coefficients of fn and give an explicit formula for the projector fn. {\textcopyright} 2025 World Scientific Publishing Company.",
keywords = "recurrence formula, coefficient, Virtual Temperley–Lieb algebra, projector",
author = "Qingying Deng and Xian{\textquoteright}an Jin and Kauffman, {Louis h.}",
year = "2025",
doi = "10.1142/S0218216525500208",
language = "English",
volume = "34",
journal = "Journal of Knot Theory and its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "5",

}

RIS

TY - JOUR

T1 - Projectors in the virtual Temperley–Lieb algebra

AU - Deng, Qingying

AU - Jin, Xian’an

AU - Kauffman, Louis h.

PY - 2025

Y1 - 2025

N2 - In this paper, we present a method of defining projectors in the virtual Temperley-Lieb algebra, that generalizes the Jones-Wenzl projectors in Temperley-Lieb algebra. We show that the projectors have similar properties with the Jones-Wenzl projectors, and contain an extra property which is associated with the virtual generator elements, that is, the product of a projector with a virtual generator is unchanged. We also show the uniqueness of the projector fn in terms of its axiomatic properties in the virtual Temperley-Lieba algebra VTLn(d). Finally, we find the coefficients of fn and give an explicit formula for the projector fn. © 2025 World Scientific Publishing Company.

AB - In this paper, we present a method of defining projectors in the virtual Temperley-Lieb algebra, that generalizes the Jones-Wenzl projectors in Temperley-Lieb algebra. We show that the projectors have similar properties with the Jones-Wenzl projectors, and contain an extra property which is associated with the virtual generator elements, that is, the product of a projector with a virtual generator is unchanged. We also show the uniqueness of the projector fn in terms of its axiomatic properties in the virtual Temperley-Lieba algebra VTLn(d). Finally, we find the coefficients of fn and give an explicit formula for the projector fn. © 2025 World Scientific Publishing Company.

KW - recurrence formula

KW - coefficient

KW - Virtual Temperley–Lieb algebra

KW - projector

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105001555199&origin=inward&txGid=3234a9951191a599c2f5f896c5b88e70

U2 - 10.1142/S0218216525500208

DO - 10.1142/S0218216525500208

M3 - Article

VL - 34

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 5

M1 - 2550020

ER -

ID: 65168096