Quantum Algebra

Authors and titles for March 2025

[1] arXiv:2503.00006 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Classification of states on certain orthomodular structures Show Chinese title

Title: 状态在某些正交模结构上的分类

Lavinia Corina Ciungu

Subjects: Quantum Algebra (math.QA)

[2] arXiv:2503.00628 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: Stated Skein Theory and Double Affine Hecke Algebra Representations Show Chinese title

Title: 陈述的绳结理论和双仿射赫克代数表示

Raymond Matson

Comments: 142(-2) pages, 20 figures, published to ProQuest

Subjects: Quantum Algebra (math.QA) ; Geometric Topology (math.GT)

[3] arXiv:2503.02945 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: Towards a complexity-theoretic dichotomy for TQFT invariants Show Chinese title

Title: 关于拓扑量子场论不变量的复杂性理论二分法

Nicolas Bridges (Purdue), Eric Samperton (Purdue)

Comments: 16 pages, 11 figures. Comments welcome!

Subjects: Quantum Algebra (math.QA) ; Computational Complexity (cs.CC) ; Geometric Topology (math.GT) ; Quantum Physics (quant-ph)

[4] arXiv:2503.03004 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: Large $N$ Vertex Algebras via Deligne Category Show Chinese title

Title: 大型 $N$顶点代数与德林德尔范畴

Keyou Zeng

Comments: 48 pages

Subjects: Quantum Algebra (math.QA) ; High Energy Physics - Theory (hep-th) ; Mathematical Physics (math-ph)

[5] arXiv:2503.03181 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: A Drinfeld Presentation of the Queer Super-Yangian Show Chinese title

Title: 一个Drinfeld形式的奇异性超Yangian

Zhihua Chang, Yongjie Wang

Comments: 33 pages, comments welcome

Subjects: Quantum Algebra (math.QA) ; Representation Theory (math.RT)

[6] arXiv:2503.03448 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Heat semigroups on quantum automorphism groups of finite dimensional C*-algebras Show Chinese title

Title: 有限维 C*-代数的量子自同构群上的热半群

Futaba Sato

Subjects: Quantum Algebra (math.QA) ; Mathematical Physics (math-ph) ; Functional Analysis (math.FA) ; Operator Algebras (math.OA)

[7] arXiv:2503.05440 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: A path description for $\varepsilon$-characters of representations of type $A$ restricted quantum loop algebras at roots of unity Show Chinese title

Title: 关于类型$\varepsilon$的表示在单位根处的限制量子环路代数的$A$-特征的一个路径描述

Xiao-Juan An, Jian-Rong Li, Yan-Feng Luo, Wen-Ting Zhang

Subjects: Quantum Algebra (math.QA)

[8] arXiv:2503.05553 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Genus $g$ Virasoro Correlation Functions for Vertex Operator Algebras Show Chinese title

Title: genus $g$ 置换算子代数的Virasoro相关函数

Michael P. Tuite, Michael Welby

Comments: 23 pages

Subjects: Quantum Algebra (math.QA) ; High Energy Physics - Theory (hep-th)

[9] arXiv:2503.05960 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: The Six-Vertex Yang-Baxter Groupoid Show Chinese title

Title: 六顶点杨-巴克斯特群oid

Daniel Bump, Slava Naprienko

Subjects: Quantum Algebra (math.QA)

[10] arXiv:2503.06280 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: On the category of Hopf braces Show Chinese title

Title: 关于Hopf braces范畴的研究

Ana Agore, Alexandru Chirvasitu

Comments: 13 pages + references

Subjects: Quantum Algebra (math.QA) ; Category Theory (math.CT) ; Rings and Algebras (math.RA)

[11] arXiv:2503.06417 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: A conjecture on monomial realizations and polyhedral realizations for crystal bases Show Chinese title

Title: 关于晶体基的单项式实现和多面体实现的一个猜想

Yuki Kanakubo

Comments: 30 pages

Subjects: Quantum Algebra (math.QA) ; Combinatorics (math.CO) ; Representation Theory (math.RT)

[12] arXiv:2503.06731 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: On the Representation Categories of Weak Hopf Algebras Arising from Levin-Wen Models Show Chinese title

Title: 论 Levin-Wen 模型中弱 Hopf 代数的表示范畴

Ansi Bai, Zhi-Hao Zhang

Comments: 58 pages, 0 figures, with an appendix on Ocneanu's tube algebras

Subjects: Quantum Algebra (math.QA) ; Strongly Correlated Electrons (cond-mat.str-el) ; High Energy Physics - Theory (hep-th) ; Mathematical Physics (math-ph) ; Category Theory (math.CT)

[13] arXiv:2503.07301 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: E(n)-coactions on semisimple Clifford algebras Show Chinese title

Title: E(n)在半单Clifford代数上的余作用

Fabio Renda

Comments: 30 pages

Subjects: Quantum Algebra (math.QA) ; Rings and Algebras (math.RA) ; Representation Theory (math.RT)

[14] arXiv:2503.08770 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: 1-shifted Lie bialgebras and their quantizations Show Chinese title

Title: 1-平移的李双代数及其量子化

Wenjun Niu, Victor Py

Comments: Comments are welcome!

Subjects: Quantum Algebra (math.QA) ; Mathematical Physics (math-ph) ; Representation Theory (math.RT)

[15] arXiv:2503.08839 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: Tensor products, $q$-characters and $R$-matrices for quantum toroidal algebras Show Chinese title

Title: 张量积，量子 toroidal 代数的$q$- 特征和$R$- 矩阵

Duncan Laurie

Comments: 93 pages, comments very welcome! v2: added work on q-characters; extended everything to final untwisted affine type; minor historical correction

Subjects: Quantum Algebra (math.QA) ; Mathematical Physics (math-ph) ; Rings and Algebras (math.RA) ; Representation Theory (math.RT)

[16] arXiv:2503.09845 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: Intertwiners of representations of untwisted quantum affine algebras and Yangians revisited Show Chinese title

Title: 未扭曲量子仿射代数和杨氏代数表示的交织算子的重新研究

Keshav Dahiya, Evgeny Mukhin

Comments: Latex, 43 pages, 10 figures

Journal-ref: Journal of Mathematical Physics, 1 May 2025; 66 (5): 051701

Subjects: Quantum Algebra (math.QA) ; Mathematical Physics (math-ph)

[17] arXiv:2503.09921 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: On the category $\mathcal{O}$ for generalized Weyl algebras Show Chinese title

Title: 关于广义Weyl代数的范畴$\mathcal{O}$

Ruben Mamani Velasco, Akaki Tikaradze

Comments: Preliminary version, 9 pages, all comments welcome

Subjects: Quantum Algebra (math.QA)

[18] arXiv:2503.10327 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: Structure groupoids of quiver-theoretic Yang-Baxter maps Show Chinese title

Title: 图论的Yang-Baxter映射的结构范畴

Davide Ferri, Youichi Shibukawa

Comments: 43 pages, 10 figures

Subjects: Quantum Algebra (math.QA)

[19] arXiv:2503.12716 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Intertwiners of representations of twisted quantum affine algebras Show Chinese title

Title: 扭曲量子仿射代数表示的交织算子

Keshav Dahiya, Evgeny Mukhin

Comments: 24 pages. arXiv admin note: substantial text overlap with arXiv:2503.09845

Journal-ref: Journal of Mathematical Physics, 1 May 2025; 66 (5): 051703

Subjects: Quantum Algebra (math.QA) ; Mathematical Physics (math-ph)

[20] arXiv:2503.13641 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Interpolation categories for Conformal Embeddings Show Chinese title

Title: 共形嵌入的插值类别

Cain Edie-Michell, Noah Snyder

Comments: 29 pages

Subjects: Quantum Algebra (math.QA) ; Operator Algebras (math.OA) ; Representation Theory (math.RT)

[21] arXiv:2503.14165 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Pre-Lie 2-bialgebras and 2-grade classical Yang-Baxter equations Show Chinese title

Title: Pre-Lie 2-bialgebras 和 2-阶经典 Yang-Baxter 方程

Jiefeng Liu, Tongtong Yue, Qi Wang

Comments: 33 pages

Subjects: Quantum Algebra (math.QA)

[22] arXiv:2503.14596 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: Continuous Tambara-Yamagami tensor categories Show Chinese title

Title: 连续Tambara-Yamagami张量范畴

Adrià Marín-Salvador

Comments: 43 pages

Subjects: Quantum Algebra (math.QA) ; High Energy Physics - Theory (hep-th) ; Category Theory (math.CT) ; Operator Algebras (math.OA)

[23] arXiv:2503.15104 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Finite Gröbner bases for quantum symmetric groups Show Chinese title

Title: 量子对称群的有限Gröbner基

Leonard Schmitz, Marcel Wack

Subjects: Quantum Algebra (math.QA) ; Rings and Algebras (math.RA)

[24] arXiv:2503.15241 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Compatible root graded anti-pre-Lie algebraic structures on finite-dimensional complex simple Lie algebras Show Chinese title

Title: 有限维复单李代数上的相容根分级反前李代数结构

Chengming Bai, Dongfang Gao

Comments: 18 pages

Subjects: Quantum Algebra (math.QA) ; Rings and Algebras (math.RA) ; Representation Theory (math.RT)

[25] arXiv:2503.15872 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: A Cousin Complex for the Quantum Projective Space Show Chinese title

Title: 量子射影空间的Cousin复形

Kobi Kremnizer, David Ssevviiri

Comments: 11 pages

Subjects: Quantum Algebra (math.QA) ; Algebraic Geometry (math.AG) ; Representation Theory (math.RT)

[26] arXiv:2503.17131 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: The triconnected Kontsevich graph complex Show Chinese title

Title: 三连通康采维奇图复形

Thomas Willwacher

Subjects: Quantum Algebra (math.QA) ; Algebraic Topology (math.AT)

[27] arXiv:2503.18630 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Actions of Fusion Categories on Path Algebras Show Chinese title

Title: 融合范畴对路径代数的作用

Alexander Betz

Comments: Comments Welcome!

Subjects: Quantum Algebra (math.QA) ; Rings and Algebras (math.RA) ; Representation Theory (math.RT)

[28] arXiv:2503.19532 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Non-factorizable ribbon Hopf Algebras Show Chinese title

Title: 不可分解的带状Hopf代数

Quentin Faes, Maksymilian Manko

Comments: 39 pages, minor modifications of Definition 2.11 and Definition 2.20, some typos corrected

Subjects: Quantum Algebra (math.QA) ; Geometric Topology (math.GT)

[29] arXiv:2503.19830 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: On the bridgeless graph complex Show Chinese title

Title: 关于无桥图复形

Thomas Willwacher

Subjects: Quantum Algebra (math.QA) ; Algebraic Topology (math.AT)

[30] arXiv:2503.20905 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: Non-semisimple WRT at the boundary of Crane-Yetter Show Chinese title

Title: 非半单WRT在Crane-Yetter边界处

Benjamin Haïoun

Comments: Many figures. Comments welcome!

Subjects: Quantum Algebra (math.QA) ; Category Theory (math.CT) ; Geometric Topology (math.GT)

[31] arXiv:2503.21265 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Exact module categories over $\mathrm{Rep}(u_q(\mathfrak{sl}_2))$ Show Chinese title

Title: 关于$\mathrm{Rep}(u_q(\mathfrak{sl}_2))$的精确模范畴

Daisuke Nakamura, Taiki Shibata (Okayama University of Science), Kenichi Shimizu (Shibaura Institute of Technology)

Comments: 49 pages

Subjects: Quantum Algebra (math.QA) ; Category Theory (math.CT) ; Representation Theory (math.RT)

[32] arXiv:2503.21390 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Vertex F-algebras and their associated Lie algebra Show Chinese title

Title: 顶点F-代数及其相关的李代数

Markus Upmeier

Comments: 20 pages

Subjects: Quantum Algebra (math.QA)

[33] arXiv:2503.22535 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: Shuffle algebras and their integral forms: specialization map approach in types $C_n$ and $D_n$ Show Chinese title

Title: 混洗代数及其积分形式：$C_n$ 和 $D_n$ 类型中的特殊化映射方法

Yue Hu, Alexander Tsymbaliuk

Comments: v1: 55 pages, comments are welcome! arXiv admin note: text overlap with arXiv:2305.00810

Subjects: Quantum Algebra (math.QA) ; Rings and Algebras (math.RA) ; Representation Theory (math.RT)

[34] arXiv:2503.23632 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: Quasi-triangular decomposition and induced modules for vertex operator algebras Show Chinese title

Title: 拟三角分解和顶点算子代数的诱导模

Jianqi Liu

Subjects: Quantum Algebra (math.QA) ; Representation Theory (math.RT)

[35] arXiv:2503.23995 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: Analytic Conformal Blocks of $C_2$-cofinite Vertex Operator Algebras III: The Sewing-Factorization Theorems Show Chinese title

Title: 解析共形块的$C_2$-有限顶点算子代数 III：缝合-分解定理

Bin Gui, Hao Zhang

Comments: 64 pages. In this revision, we explain why the fusion product of V along the torus equals Lyubashenko's coend, as previously claimed in Section 0.6 of the earlier versions

Subjects: Quantum Algebra (math.QA) ; Mathematical Physics (math-ph) ; Representation Theory (math.RT)

[36] arXiv:2503.24348 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: On the unitarity and modularity of ribbon tensor categories associated with affine Lie algebras Show Chinese title

Title: 关于与仿射李代数相关的胶带张量范畴的单位性和模性

Daria Rudneva, Eddy Ardonne

Comments: 10 pages

Subjects: Quantum Algebra (math.QA)

[37] arXiv:2503.00105 (cross-list from cond-mat.str-el) [cn-pdf, pdf, html, other]

Title: Anomalies of Coset Non-Invertible Symmetries Show Chinese title

Title: 共轭非可逆对称性的异常

Po-Shen Hsin, Ryohei Kobayashi, Carolyn Zhang

Comments: 39 pages, 5 figures. Updated discussions in Sec.2.3, minor revisions

Subjects: Strongly Correlated Electrons (cond-mat.str-el) ; High Energy Physics - Theory (hep-th) ; Quantum Algebra (math.QA)

[38] arXiv:2503.00275 (cross-list from math.RT) [cn-pdf, pdf, html, other]

Title: Rainbow Boomerang Graphs Show Chinese title

Title: 彩虹回旋镖图

Shunsuke Hirota

Comments: arXiv admin note: substantial text overlap with arXiv:2502.14274

Subjects: Representation Theory (math.RT) ; Quantum Algebra (math.QA)

[39] arXiv:2503.00829 (cross-list from math-ph) [cn-pdf, pdf, html, other]

Title: Multispecies inhomogeneous $t$-PushTASEP from antisymmetric fusion Show Chinese title

Title: 多物种非均匀$t$-PushTASEP 来自反对称融合

Arvind Ayyer, Atsuo Kuniba

Comments: 22 pages, 4 figures, minor improvements

Subjects: Mathematical Physics (math-ph) ; Combinatorics (math.CO) ; Probability (math.PR) ; Quantum Algebra (math.QA)

[40] arXiv:2503.01240 (cross-list from math.OA) [cn-pdf, pdf, html, other]

Title: Hormander-Mikhlin type theorem on non-commutative spaces Show Chinese title

Title: 非交换空间上的Hormander-Mikhlin型定理

Rauan Akylzhanov, Michael Ruzhansky, Kanat Tulenov

Comments: 18 pages

Subjects: Operator Algebras (math.OA) ; Quantum Algebra (math.QA)

[41] arXiv:2503.01366 (cross-list from math.GR) [cn-pdf, pdf, html, other]

Title: Analogs of the lower and upper central series in skew braces: a survey Show Chinese title

Title: 斜括号中下和上中心序列的类比：综述

Cindy Tsang

Comments: 30 pages; updated final version (the numbering of equations has been changed according to the journal's requirement)

Subjects: Group Theory (math.GR) ; Quantum Algebra (math.QA)

[42] arXiv:2503.01501 (cross-list from math.OA) [cn-pdf, pdf, html, other]

Title: Quantum metrics from length functions on quantum groups Show Chinese title

Title: 量子群上的长度函数的量子度量

Are Austad, David Kyed

Comments: 29 pages. Minor changes and clarifications added

Subjects: Operator Algebras (math.OA) ; Quantum Algebra (math.QA)

[43] arXiv:2503.02020 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: A complex of ribbon quivers and $\mathcal{M}_{g,m}$ Show Chinese title

Title: 一个带有丝带箭图的复形和$\mathcal{M}_{g,m}$

Sergei Merkulov

Comments: In v2 the definition of the derivation complex given in Section 5 is rewritten in a more detailed and explicit way. Some misprints are corrected

Subjects: Algebraic Geometry (math.AG) ; Quantum Algebra (math.QA)

[44] arXiv:2503.03445 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: Duoidal R-Matrices Show Chinese title

Title: 双幺矩阵

Tony Zorman

Comments: 16 pages, comments welcome!

Subjects: Category Theory (math.CT) ; Quantum Algebra (math.QA)

[45] arXiv:2503.03827 (cross-list from quant-ph) [cn-pdf, pdf, other]

Title: Generalized toric codes on twisted tori for quantum error correction Show Chinese title

Title: 广义环面码在扭曲环面上的量子纠错应用

Zijian Liang, Ke Liu, Hao Song, Yu-An Chen

Comments: 14+9 pages, 4 figures; v3: typos fixed

Subjects: Quantum Physics (quant-ph) ; Strongly Correlated Electrons (cond-mat.str-el) ; Mathematical Physics (math-ph) ; Quantum Algebra (math.QA)

[46] arXiv:2503.04297 (cross-list from math.AT) [cn-pdf, pdf, other]

Title: Properadic coformality of spheres Show Chinese title

Title: 球体的适当代数余形式性

Coline Emprin, Alex Takeda

Comments: 29 pages, comments are welcome

Subjects: Algebraic Topology (math.AT) ; Quantum Algebra (math.QA)

[47] arXiv:2503.05307 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Derived deformation functors, Koszul duality, and Maurer-Cartan spaces Show Chinese title

Title: 衍生形变函子，Koszul对偶性，Maurer-Cartan空间

J.P.Pridham

Comments: 16pp., survey with some new material; v2 final version, to appear in Philosophical Transactions of the Royal Society A

Subjects: Algebraic Geometry (math.AG) ; Algebraic Topology (math.AT) ; Quantum Algebra (math.QA)

[48] arXiv:2503.05317 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Derived derivations govern contraderived deformations of dg algebras over dg (pr)operads Show Chinese title

Title: 导出导数支配dg代数关于dg (pr)operads的反导数变形

J. P. Pridham

Comments: 17pp, two independent proofs

Subjects: Algebraic Geometry (math.AG) ; Quantum Algebra (math.QA)

[49] arXiv:2503.05342 (cross-list from math.GT) [cn-pdf, pdf, other]

Title: Framed Braid Equivalences Show Chinese title

Title: 框架辫等价

Anastasios Kokkinakis

Comments: 30 pages, 35 figures

Subjects: Geometric Topology (math.GT) ; Group Theory (math.GR) ; Quantum Algebra (math.QA)

[50] arXiv:2503.05975 (cross-list from hep-th) [cn-pdf, pdf, html, other]

Title: The Nilpotency Index for 4d $\mathcal{N}=2$ SCFTs Show Chinese title

Title: 4d $\mathcal{N}=2$ SCFTs 的幂零指数

Anirudh Deb, Carlo Meneghelli, Leonardo Rastelli

Comments: 29 pages, 3 tables, 1 figure

Subjects: High Energy Physics - Theory (hep-th) ; Mathematical Physics (math-ph) ; Quantum Algebra (math.QA)