arXiv - MATH - Quantum Algebra最新文献

Semisimplicity of module categories of certain affine vertex operator superalgebras 某些仿射顶点算子上代数的模类半简约性

arXiv - MATH - Quantum Algebra Pub Date : 2024-09-18 DOI: arxiv-2409.11797

Dražen Adamović, Chunrui Ai, Xingjun Lin, Jinwei Yang

引用次数: 0

Basic monodromy operator for quantum superalgebra 量子超代数的基本单色算子

arXiv - MATH - Quantum Algebra Pub Date : 2024-09-17 DOI: arxiv-2409.11097

A. V. Razumov

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Evaluation 2-Functors for Kac-Moody 2-Categories of Type A2 A2 型 Kac-Moody 2 类的评价 2 函数

arXiv - MATH - Quantum Algebra Pub Date : 2024-09-16 DOI: arxiv-2409.10434

Marco Mackaay, James Macpherson, Pedro Vaz

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Bimodules over twisted Zhu algebras and a construction of tensor product of twisted modules for vertex operator algebras 扭曲朱代数上的双模和顶点算子代数扭曲模块张量积的构建

arXiv - MATH - Quantum Algebra Pub Date : 2024-09-13 DOI: arxiv-2409.08995

Yiyi Zhu

{"title":"Bimodules over twisted Zhu algebras and a construction of tensor product of twisted modules for vertex operator algebras","authors":"Yiyi Zhu","doi":"arxiv-2409.08995","DOIUrl":"https://doi.org/arxiv-2409.08995","url":null,"abstract":"Let $V$ be a simple, non-negatively-graded, rational, $C_2$-cofinite, and\u0000self dual vertex operator algebra, $g_1, g_2, g_3$ be three commuting finitely\u0000ordered automorphisms of $V$ such that $g_1g_2=g_3$ and $g_i^T=1$ for $i=1, 2,\u00003$ and $Tin N$. Suppose $M^1$ is a $g_1$-twisted module. For any $n, min\u0000frac{1}{T}N$, we construct an $A_{g_3, n}(V)$-$A_{g_2, m}(V)$-bimodule\u0000$mathcal{A}_{g_3, g_2, n, m}(M^1)$ associated to the quadruple $(M^1, g_1,\u0000g_2, g_3)$. Given an $A_{g_2, m}(V)$-module $U$, an admissible $g_3$-twisted\u0000module $mathcal{M}(M^1, U)$ is constructed. For the quadruple $(V, 1, g, g)$\u0000for some $gin text{Aut}(V)$, $mathcal{A}_{g, g, n, m}(V)$ coincides with the\u0000$A_{g, n}(V)$-$A_{g, m}(V)$-bimodules $A_{g, n, m}(V)$ constructed by\u0000Dong-Jiang, and $mathcal{M}(V, U)$ is the generalized Verma type admissible\u0000$g$-twisted module generated by $U$. For an irreducible $g_1$-twisted module\u0000$M^1$ and an irreducible $g_2$-twisted module $M^2$, we give a construction of\u0000tensor product of $M^1$ and $M^2$ using the bimodule theory developed in this\u0000paper. As an application, a twisted version of the fusion rules theorem is\u0000established.","PeriodicalId":501317,"journal":{"name":"arXiv - MATH - Quantum Algebra","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Poisson brackets and coaction maps of regularized holonomies of the KZ equation KZ 方程正则化整体的泊松括号和协迫映射

arXiv - MATH - Quantum Algebra Pub Date : 2024-09-13 DOI: arxiv-2409.08894

Anton Alekseev, Florian Naef, Muze Ren

引用次数: 0

Non-unitary Wightman CFTs and non-unitary vertex algebras 非统一维特曼 CFT 和非统一顶点代数

arXiv - MATH - Quantum Algebra Pub Date : 2024-09-13 DOI: arxiv-2409.08454

Sebastiano Carpi, Christopher Raymond, Yoh Tanimoto, James E. Tener

引用次数: 0

Bootstrapping the critical behavior of multi-matrix models 引导多矩阵模型的临界行为

arXiv - MATH - Quantum Algebra Pub Date : 2024-09-11 DOI: arxiv-2409.07565

Masoud Khalkhali, Nathan Pagliaroli, Andrei Parfeni, Brayden Smith

{"title":"Bootstrapping the critical behavior of multi-matrix models","authors":"Masoud Khalkhali, Nathan Pagliaroli, Andrei Parfeni, Brayden Smith","doi":"arxiv-2409.07565","DOIUrl":"https://doi.org/arxiv-2409.07565","url":null,"abstract":"Given a matrix model, by combining the Schwinger-Dyson equations with\u0000positivity constraints on its solutions, in the large $N$ limit one is able to\u0000obtain explicit and numerical bounds on its moments. This technique is known as\u0000bootstrapping with positivity. In this paper we use this technique to estimate\u0000the critical points and exponents of several matrix multi-models. As a proof of\u0000concept, we first show it can be used to find the well-studied quartic single\u0000matrix model's critical phenomena. We then apply the method to several similar\u0000``unsolved\" 2-matrix models with various quartic interactions. We conjecture\u0000and present strong evidence for the string susceptibility exponent for some of\u0000these models to be $gamma = 1/2$, which heuristically indicates that the\u0000continuum limit will likely be the Continuum Random Tree. For the other\u00002-matrix models, we find estimates of new string susceptibility exponents that\u0000may indicate a new continuum limit. We then study an unsolved 3-matrix model\u0000that generalizes the 3-colour model with cubic interactions. Additionally, for\u0000all of these models, we are able to derive explicitly the first several terms\u0000of the free energy in the large $N$ limit as a power series expansion in the\u0000coupling constants at zero by exploiting the structure of the Schwinger-Dyson\u0000equations.","PeriodicalId":501317,"journal":{"name":"arXiv - MATH - Quantum Algebra","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On differential Hopf algebras and $B_infty$ algebras 论微分霍普夫布拉斯和$B_infty$布拉斯

arXiv - MATH - Quantum Algebra Pub Date : 2024-09-10 DOI: arxiv-2409.06632

Imma Gálvez-Carrillo, María Ronco, Andy Tonks

引用次数: 0

Brownian motion on the unitary quantum group. Construction and asymptotic study 单元量子群上的布朗运动。构造和渐近研究

arXiv - MATH - Quantum Algebra Pub Date : 2024-09-10 DOI: arxiv-2409.06552

Jean Delhaye

引用次数: 0

Algebraic isomorphisms of quantized homogeneous spaces 量化同质空间的代数同构

arXiv - MATH - Quantum Algebra Pub Date : 2024-09-10 DOI: arxiv-2409.06139

Robert Yuncken

引用次数: 0