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Extended and Reshetikhin Twists for sl(3)

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Vladimir Lyakhovsky, Mariano A. del Olmo

Quantum Algebra · Submitted 11 Mar 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim These sets of deformations are in one-to-one correspondence: each element of {U_E(\theta)(sl(3))} can be obtained by a limiting procedure from the unique point in the set {U_DJR(\lambda)(sl(3))}.

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arXiv IDmath/9903065 (version 1)
Pith IDTI6DRMPC, Pith's permanent record of this paper and its review
CitationMariano A. del Olmo, Vladimir Lyakhovsky. "Extended and Reshetikhin Twists for sl(3)." arXiv:math/9903065 (1999). https://pith.science/paper/TI6DRMPC
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,549 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.46 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The properties of the set {L} of extended jordanian twists for algebra sl(3) are studied. Starting from the simplest algebraic construction --- the peripheric Hopf algebra U_ P'(0,1)(sl(3)) --- we construct explicitly the complete family of extended twisted algebras {U_ E(\theta)(sl(3))} corresponding to the set of 4-dimensional Frobenius subalgebras {L(\theta)} in sl(3). It is proved that the extended twisted algebras with different values of the parameter \theta are connected by a special kind of Reshetikhin twist. We study the relations between the family {U_E(\theta)(sl(3))} and the one-dimensional set {U_DJR(\lambda)(sl(3))} produced by the standard Reshetikhin twist from the Drinfeld--Jimbo quantization U_DJ(sl(3)). These sets of deformations are in one-to-one correspondence: each element of {U_E(\theta)(sl(3))} can be obtained by a limiting procedure from the unique point in the set {U_DJR(\lambda)(sl(3))}.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The properties of the set {L} of extended jordanian twists for algebra sl(3) are studied. contribution 0.92 0.79 0.07 asserted 0.93
s1 Starting from the simplest algebraic construction --- the peripheric Hopf algebra U_ P'(0,1)(sl(3)) --- we construct explicitly the complete family of extended twisted algebras {U_ E(\theta)(sl(3))} corresponding to the set of 4-dimensional Frobenius subalgebras {L(\theta)} in sl(3). method 0.61 0.94 0.10 asserted 1.00
s2 It is proved that the extended twisted algebras with different values of the parameter \theta are connected by a special kind of Reshetikhin twist. result 1.00 0.89 0.24 asserted 1.00
s3 We study the relations between the family {U_E(\theta)(sl(3))} and the one-dimensional set {U_DJR(\lambda)(sl(3))} produced by the standard Reshetikhin twist from the Drinfeld--Jimbo quantization U_DJ(sl(3)). contribution 0.96 0.83 0.09 asserted 0.85
s4 These sets of deformations are in one-to-one correspondence: each element of {U_E(\theta)(sl(3))} can be obtained by a limiting procedure from the unique point in the set {U_DJR(\lambda)(sl(3))}. result 1.00 0.86 0.54 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The properties of the set {L} of extended jordanian twists for algebra sl(3) are studied. Starting from the simplest algebraic construction --- the peripheric Hopf algebra U_ P'(0,1)(sl(3)) --- we construct explicitly the complete family of extended twisted algebras {U_ E(\theta)(sl(3))} corresponding to the set of 4-dimensional Frobenius subalgebras {L(\theta)} in sl(3). It is proved that the extended twisted algebras with different values of the parameter \theta are connected by a special kind of Reshetikhin twist. We study the relations between the family {U_E(\theta)(sl(3))} and the one-dimensional set {U_DJR(\lambda)(sl(3))} produced by the standard Reshetikhin twist from the Drinfeld--Jimbo quantization U_DJ(sl(3)). These sets of deformations are in one-to-one correspondence: each element of {U_E(\theta)(sl(3))} can be obtained by a limiting procedure from the unique point in the set {U_DJR(\lambda)(sl(3))}.

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