Quantum Algebra · arXiv:2104.08106 v1 · submitted 16 Apr 2021
The alternating central extension of the Onsager Lie algebra
The paper says
“In this paper we introduce a Lie algebra 𝒪 that is roughly described by the following two analogies: (i) 𝒪 is to O as 𝒪q is to Oq; (ii) Oq is to O as 𝒪q is to 𝒪.”
from the abstract · picked out as the main claim by a classifier
Reviews
Reviews by people
No person has reviewed this paper on Pith yet. A scientist listed on Pith can review it for a fee, and their review is published here whatever it concludes.
The paper
Abstract
The Onsager Lie algebra O is often used to study integrable lattice models. The universal enveloping algebra of O admits a q-deformation Oq called the q-Onsager algebra. Recently, an algebra 𝒪q was introduced called the alternating central extension of Oq. In this paper we introduce a Lie algebra 𝒪 that is roughly described by the following two analogies: (i) 𝒪 is to O as 𝒪q is to Oq; (ii) Oq is to O as 𝒪q is to 𝒪. We call 𝒪 the alternating central extension of O. This paper contains a comprehensive description of 𝒪.
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. No sentence in this record was written by a model.
abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 0.66
What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.72 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| The Onsager Lie algebra $O$ is often used to study integrable lattice models. | background 1.00 | 0.04 | 0.02 | asserted 0.96 |
| The universal enveloping algebra of $O$ admits a $q$-deformation $O_q$ called the $q$-Onsager algebra. | background 1.00 | 0.05 | 0.03 | asserted 1.00 |
| Recently, an algebra $\mathcal O_q$ was introduced called the alternating central extension of $O_q$. | background 1.00 | 0.06 | 0.05 | asserted 1.00 |
| In this paper we introduce a Lie algebra $\mathcal O$ that is roughly described by the following two analogies: (i) $\mathcal O$ is to $O$ as $\mathcal O_q$ is to $O_q$; (ii) $O_q$ is to $O$ as $\mathcal O_q$ is to $\mathcal O$. | contribution 0.98 | 0.78 | 0.20 | asserted 0.66 |
| We call $\mathcal O$ the alternating central extension of $O$. | contribution 0.98 | 0.82 | 0.23 | asserted 1.00 |
| This paper contains a comprehensive description of $\mathcal O$. | contribution 1.00 | 0.74 | 0.16 | asserted 1.00 |
What kind of paper the classifier reports this is: theoretical result 0.88 · evidence from proof or derivation 0.86
What was examined, and what was not
Sources read
- arXiv listing abstract v1
Not examined
- full text
- figures and tables
- references and citing sentences
- relations to other papers
Levels run
- P abstract
Not run
- S sections
- T body sentences
- C citations
- R cross-paper relations
How the labels were made
Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,909 input tokens.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
Cited by 1 Pith paper
Reviewed papers on Pith that cite this one. The full citation record
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 41 sentences without a confident label
Uses the method or tool of 2 papers
-
These implications can be obtained by adapting the proof of [ref] .
The alternating presentation of $U_q(\widehat{gl_2})$ from Freidel-Maillet algebras · The Onsager Lie algebra · 0.93
-
This presentation is used in [ref] to obtain an attractive basis for $O$; see Lemma [ref] below.
FRT presentation of classical Askey-Wilson algebras · Introduction · 0.93
Compares with 2 papers
-
The analogous presentations of $𝒪_q$ can be found in [ref] and [ref] .
The compact presentation for the alternating central extension of the $q$-Onsager algebra · How $O$ and $𝒪$ are related to $O_q$ and $𝒪_q$ · 0.84
-
The elements $W_-k$, $W_k+1$, $G̃_k+1$ in Lemma [ref] correspond to the elements called $W_-k/2$, $W_k+1/2$, $G̃_k+1/4$ in [ref] .
FRT presentation of classical Askey-Wilson algebras · The Onsager Lie algebra · 0.94
Cites as background 31 papers
-
(See [ref] , [ref] .) Define the algebra $𝒪_q$ by generators [equation] and the following relations.
A new (in)finite dimensional algebra for quantum integrable models · How $O$ and $𝒪$ are related to $O_q$ and $𝒪_q$ · 0.81
-
(See [ref] , [ref] .) Define the algebra $𝒪_q$ by generators [equation] and the following relations.
A new current algebra and the reflection equation · How $O$ and $𝒪$ are related to $O_q$ and $𝒪_q$ · 0.81
-
Via this presentation, the universal enveloping algebra of $O$ admits a $q$-deformation $O_q$ called the $q$-Onsager algebra [ref] , [ref] .
Deformed Dolan-Grady relations in quantum integrable models · Introduction · 0.81
Challenges and discussion
Know something about this paper? Leave a comment.
Come back by email
A short list of the week's newly reviewed papers. Nothing is sent until you confirm from your inbox, and every email has a link that stops it. No account.
No comments yet.
Sign in to comment