arXiv - MATH - Quantum Algebra最新文献_第6页

Conformal limits in Cayley components and $Θ$-positive opers Cayley 分量中的共形极限和 $Θ$ 正 opers

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-12 DOI: arxiv-2408.06198

Georgios Kydonakis, Mengxue Yang

引用次数: 0

Flatness of $α$-induced bi-unitary connections and commutativity of Frobenius algebras α$引起的双单元连接的平坦性与弗罗贝尼斯代数的交换性

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-10 DOI: arxiv-2408.05501

Yasuyuki Kawahigashi

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Amenable actions of compact and discrete quantum groups on von Neumann algebras 紧凑和离散量子群在冯-诺依曼代数上的可修正作用

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-10 DOI: arxiv-2408.05571

K. De Commer, J. De Ro

{"title":"Amenable actions of compact and discrete quantum groups on von Neumann algebras","authors":"K. De Commer, J. De Ro","doi":"arxiv-2408.05571","DOIUrl":"https://doi.org/arxiv-2408.05571","url":null,"abstract":"Let $mathbb{G}$ be a compact quantum group and $Asubseteq B$ an inclusion\u0000of $sigma$-finite $mathbb{G}$-dynamical von Neumann algebras. We prove that\u0000the $mathbb{G}$-inclusion $Asubseteq B$ is strongly equivariantly amenable if\u0000and only if it is equivariantly amenable, using techniques from the theory of\u0000non-commutative $L^p$-spaces. In particular, if $(A, alpha)$ is a\u0000$mathbb{G}$-dynamical von Neumann algebra with $A$ $sigma$-finite, the action\u0000$alpha: A curvearrowleft mathbb{G}$ is strongly (inner) amenable if and only\u0000if the action $alpha: A curvearrowleft mathbb{G}$ is (inner) amenable. By\u0000duality, we also obtain the same result for $mathbb{G}$ a discrete quantum\u0000group, so that, in particular, a discrete quantum group is inner amenable if\u0000and only it is strongly inner amenable. This result can be seen as a dynamical\u0000generalization of Tomatsu's result on the amenability/co-amenability duality.\u0000We provide an example of a co-amenable (non-Kac) compact quantum group that\u0000acts non-amenably on a von Neumann algebra. By duality, this gives an explicit\u0000example of an amenable discrete quantum group that acts non-amenably on a von\u0000Neumann algebra.","PeriodicalId":501317,"journal":{"name":"arXiv - MATH - Quantum Algebra","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225263","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

Twisted q-Yangians and Sklyanin determinants 扭曲的 q-Yangians 和 Sklyanin 行列式

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-08 DOI: arxiv-2408.04340

Naihuan Jing, Jian Zhang

引用次数: 0

Hopf q-braces structures on rank one pointed Hopf algebras 一阶尖霍普夫代数上的霍普夫 q 带结构

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-07 DOI: arxiv-2408.03863

Jorge A. Guccione, Juan J. Guccione, Christian Valqui

引用次数: 0

A theory of locally convex Hopf algebras 局部凸霍普夫布拉斯理论

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-07 DOI: arxiv-2408.03805

Hua Wang

{"title":"A theory of locally convex Hopf algebras","authors":"Hua Wang","doi":"arxiv-2408.03805","DOIUrl":"https://doi.org/arxiv-2408.03805","url":null,"abstract":"Using the completed inductive, projective and injective tensor products of\u0000Grothendieck for locally convex topological vector spaces, we develop a\u0000systematic theory of locally convex Hopf algebras with an emphasis on\u0000Pontryagin-type dualities. We describe how classical Hopf algebras, real and\u0000complex Lie groups, as well as compact and discrete quantum groups, can all\u0000give rise to natural examples of this theory in a variety of different ways. We\u0000also show that the space of all continuous functions on a topological group $ G\u0000$ whose topological structures are compactly generated has an $ varepsilon\u0000$-Hopf algebra structure, and we can recover $ G $ fully as a topological group\u0000from this locally convex Hopf algebra. The latter is done via a generalization\u0000of Gelfand duality, which is of its own interest. Certain projective and\u0000inductive limits are also considered in this framework, and it is shown that\u0000how this can lead to examples seemingly outside of the framework of locally\u0000compact quantum groups in the sense of Kustermans-Vaes. As an illustration, we\u0000propose a version of the infinite quantum permutation group $ S^{+}_{infty} $,\u0000the free orthogonal group $ O^{+}_{infty} $, and the free unitary group $\u0000U^{+}_{infty} $ as certain strict inductive limits, all of which still retain\u0000a nice duality. Combined with our duality theory, this may be seen as an\u0000alternative tentative approach to the Kac program of developing a\u0000Pontryagin-type duality to a wider class, while at the same time, we include\u0000many more interesting examples of classical and quantum groups.","PeriodicalId":501317,"journal":{"name":"arXiv - MATH - Quantum Algebra","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949154","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

Rationality of Lorentzian Lattice CFTs And The Associated Modular Tensor Category 洛伦兹晶格 CFT 的合理性及相关的模态张量类别

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-05 DOI: arxiv-2408.02744

Ranveer Kumar Singh, Madhav Sinha, Runkai Tao

引用次数: 0

Recovering R-symbols from modular data 从模块数据中恢复 R 符号

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-05 DOI: arxiv-2408.02748

Siu-Hung Ng, Eric C Rowell, Xiao-Gang Wen

引用次数: 0

The Cyclic and Modular Microcosm Principle in Quantum Topology 量子拓扑学中的循环和模块微观世界原理

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-05 DOI: arxiv-2408.02644

Lukas Woike

{"title":"The Cyclic and Modular Microcosm Principle in Quantum Topology","authors":"Lukas Woike","doi":"arxiv-2408.02644","DOIUrl":"https://doi.org/arxiv-2408.02644","url":null,"abstract":"Monoidal categories with additional structure such as a braiding or some form\u0000of duality abound in quantum topology. They often appear in tandem with\u0000Frobenius algebras inside them. Motivations for this range from the theory of\u0000module categories to the construction of correlators in conformal field theory.\u0000We generalize the Baez-Dolan microcosm principle to consistently describe all\u0000these types of algebras by extending it to cyclic and modular algebras in the\u0000sense of Getzler-Kapranov. Our main result links the microcosm principle for\u0000cyclic algebras to the one for modular algebras via Costello's modular\u0000envelope. The result can be understood as a local-to-global construction for\u0000various flavors of Frobenius algebras that substantially generalizes and\u0000unifies the available, and often intrinsically semisimple methods using for\u0000example triangulations, state-sum constructions or skein theory. Several\u0000applications of the main result in conformal field theory are presented: We\u0000classify consistent systems of correlators for open conformal field theories\u0000and show that the genus zero correlators for logarithmic conformal field\u0000theories constructed by Fuchs-Schweigert can be uniquely extended to\u0000handlebodies. This establishes a very general correspondence between full genus\u0000zero conformal field theory in dimension two and skein theory in dimension\u0000three.","PeriodicalId":501317,"journal":{"name":"arXiv - MATH - Quantum Algebra","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949157","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

Doubly alternating words in the positive part of $U_q(widehat{mathfrak{sl}}_2)$ $U_q(widehat{mathfrak{sl}}_2)$正部分中的双交替词

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-05 DOI: arxiv-2408.02633

Chenwei Ruan

引用次数: 0