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Loop Polynomials for Knots on a 3-Sp...

Cazes-Nasitiqui, Gonzalo,

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Loop Polynomials for Knots on a 3-Sphere /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Loop Polynomials for Knots on a 3-Sphere // Gonzalo Cazes-Nasitiqui.
Author:	Cazes-Nasitiqui, Gonzalo,
Description:	1 electronic resource (71 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
Contained By:	Dissertations Abstracts International86-11B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31769226
ISBN:	9798315703358

Loop Polynomials for Knots on a 3-Sphere /
Cazes-Nasitiqui, Gonzalo,

Loop Polynomials for Knots on a 3-Sphere /Gonzalo Cazes-Nasitiqui. - 1 electronic resource (71 pages)

Source: Dissertations Abstracts International, Volume: 86-11, Section: B.

We develop a method of calculating the first loop polynomials of a knot based on the R-matrix Reshetikhin-Turaev formula for the colored Jones and HOMFLY-PT polynomials. The method is based on (1) replacing the finite-dimensional sl2 and sl3 representations with Verma modules of the same highest weight, (2) identifying each Verma module with the polynomial algebra, one generator per positive root, (3) presenting each R-matrix as a composition of Burau-based linear transformation of polynomial variables and a series in ln q with coefficients being differential operators acting on the polynomials and, finally, (4) computing the traces of products of these operators by using a combinatorial trick commonly used in deriving the Feynman diagram rules. We present some computational results based on this method.

English

ISBN: 9798315703358Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Loop polynomials

Loop Polynomials for Knots on a 3-Sphere /
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005 20250825062320.5
006 m o d
007 cr|nu||||||||
008 261011s2025 miu||||||m |||||||eng d
020 $a 9798315703358
035 $a (MiAaPQD)AAI31769226
035 $a AAI31769226
040 $a MiAaPQD $b eng $c MiAaPQD $e rda
100 1 $a Cazes-Nasitiqui, Gonzalo, $e author. $3 3822957
245 1 0 $a Loop Polynomials for Knots on a 3-Sphere / $c Gonzalo Cazes-Nasitiqui.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (71 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
500 $a Advisors: Rozansky, Lev Committee members: Dumitrescu, Olivia; Hong, Jiuzu; Rimanyi, Richard; Varchenko, Alexander.
502 $b Ph.D. $c The University of North Carolina at Chapel Hill $d 2025.
520 $a We develop a method of calculating the first loop polynomials of a knot based on the R-matrix Reshetikhin-Turaev formula for the colored Jones and HOMFLY-PT polynomials. The method is based on (1) replacing the finite-dimensional sl2 and sl3 representations with Verma modules of the same highest weight, (2) identifying each Verma module with the polynomial algebra, one generator per positive root, (3) presenting each R-matrix as a composition of Burau-based linear transformation of polynomial variables and a series in ln q with coefficients being differential operators acting on the polynomials and, finally, (4) computing the traces of products of these operators by using a combinatorial trick commonly used in deriving the Feynman diagram rules. We present some computational results based on this method.
546 $a English
590 $a School code: 0153
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
650 4 $a Theoretical physics. $3 2144760
653 $a Loop polynomials
653 $a Quantum groups
653 $a Polynomial algebra
653 $a Feynman diagram rules
653 $a Differential operators
690 $a 0405
690 $a 0642
690 $a 0753
690 $a 0364
710 2 $a The University of North Carolina at Chapel Hill. $b Mathematics. $e degree granting institution. $3 3820964
720 1 $a Rozansky, Lev $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-11B.
790 $a 0153
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31769226