Relevant bibliographies by topics / Modular categories

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Modular categories'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Modular categories"

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Beliakova, Anna, Christian Blanchet, and Eva Contreras. "Spin modular categories." Quantum Topology 8, no. 3 (2017): 459–504. http://dx.doi.org/10.4171/qt/95.

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Lyubashenko, V. "Ribbon Abelian Categories as Modular Categories." Journal of Knot Theory and Its Ramifications 05, no. 03 (1996): 311–403. http://dx.doi.org/10.1142/s0218216596000229.

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A category N of labeled (oriented) trivalent graphs (nets) or ribbon graphs is extended by new generators called fusing, braiding, twist and switch with relations which can be called Moore-Seiberg relations. A functor to N is constructed from the category Surf of oriented surfaces with labeled boundary and their homeomorphisms. Given a (eventually non-semisimple) k-linear abelian ribbon braided category [Formula: see text] with some finiteness conditions we construct a functor from a central extension of N with the set of labels [Formula: see text] ObC to k-vector spaces. Composing the functor
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Deaton, Adam, Paul Gustafson, Leslie Mavrakis, et al. "Integral metaplectic modular categories." Journal of Knot Theory and Its Ramifications 29, no. 05 (2020): 2050032. http://dx.doi.org/10.1142/s0218216520500327.

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A braided fusion category is said to have Property F if the associated braid group representations factor through a finite group. We verify integral metaplectic modular categories have property F by showing these categories are group-theoretical. For the special case of integral categories [Formula: see text] with the fusion rules of [Formula: see text] we determine the finite group [Formula: see text] for which [Formula: see text] is braided equivalent to [Formula: see text]. In addition, we determine the associated classical link invariant, an evaluation of the 2-variable Kauffman polynomial
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Bonderson, Parsa, Colleen Delaney, César Galindo, Eric C. Rowell, Alan Tran, and Zhenghan Wang. "On invariants of modular categories beyond modular data." Journal of Pure and Applied Algebra 223, no. 9 (2019): 4065–88. http://dx.doi.org/10.1016/j.jpaa.2018.12.017.

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Bruillard, Paul, Siu-Hung Ng, Eric C. Rowell, and Zhenghan Wang. "Rank-finiteness for modular categories." Journal of the American Mathematical Society 29, no. 3 (2015): 857–81. http://dx.doi.org/10.1090/jams/842.

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HONG, SEUNG-MOON, ERIC ROWELL, and ZHENGHAN WANG. "ON EXOTIC MODULAR TENSOR CATEGORIES." Communications in Contemporary Mathematics 10, supp01 (2008): 1049–74. http://dx.doi.org/10.1142/s0219199708003162.

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It has been conjectured that every (2 + 1)-TQFT is a Chern-Simons-Witten (CSW) theory labeled by a pair (G, λ), where G is a compact Lie group, and λ ∈ H4(BG; ℤ) a cohomology class. We study two TQFTs constructed from Jones' subfactor theory which are believed to be counterexamples to this conjecture: one is the quantum double of the even sectors of the E6subfactor, and the other is the quantum double of the even sectors of the Haagerup subfactor. We cannot prove mathematically that the two TQFTs are indeed counterexamples because CSW TQFTs, while physically defined, are not yet mathematically
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Lyubashenko, V. "Modular transformations for tensor categories." Journal of Pure and Applied Algebra 98, no. 3 (1995): 279–327. http://dx.doi.org/10.1016/0022-4049(94)00045-k.

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Kirillov, Jr., Alexander. "Modular Categories and Orbifold Models." Communications in Mathematical Physics 229, no. 2 (2002): 309–35. http://dx.doi.org/10.1007/s002200200650.

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Ardonne, Eddy, Meng Cheng, Eric C. Rowell, and Zhenghan Wang. "Classification of metaplectic modular categories." Journal of Algebra 466 (November 2016): 141–46. http://dx.doi.org/10.1016/j.jalgebra.2016.08.001.

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Takeuchi, Mitsuhiro. "Modular Categories and Hopf Algebras." Journal of Algebra 243, no. 2 (2001): 631–43. http://dx.doi.org/10.1006/jabr.2001.8856.

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Dissertations / Theses on the topic "Modular categories"

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Hauge, Martin. "Triangulated categories in modular representation theory and their direct sum decompositions." Thesis, University of Bristol, 2017. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.723477.

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Wang, Yilong. "On Integrality of SO(n)-Level 2 TQFTs." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1525703476442228.

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Ohrmann, Tobias [Verfasser], and Christoph [Akademischer Betreuer] Schweigert. "Non-semisimple modular tensor categories from small quantum groups / Tobias Ohrmann ; Betreuer: Christoph Schweigert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2018. http://d-nb.info/1169358497/34.

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Ohrmann, Tobias Verfasser], and Christoph [Akademischer Betreuer] [Schweigert. "Non-semisimple modular tensor categories from small quantum groups / Tobias Ohrmann ; Betreuer: Christoph Schweigert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2018. http://d-nb.info/1169358497/34.

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Mierach, Svea Nora [Verfasser], and Christoph [Akademischer Betreuer] Schweigert. "Hochschild cohomology, modular tensor categories and mapping class groups / Svea Nora Mierach ; Betreuer: Christoph Schweigert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2020. http://d-nb.info/1216998140/34.

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Mierach, Svea Nora Verfasser], and Christoph [Akademischer Betreuer] [Schweigert. "Hochschild cohomology, modular tensor categories and mapping class groups / Svea Nora Mierach ; Betreuer: Christoph Schweigert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2020. http://d-nb.info/1216998140/34.

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Wasserman, Thomas A. "A reduced tensor product of braided fusion categories over a symmetric fusion category." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:58c6aae3-cb0e-4381-821f-f7291ff95657.

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The main goal of this thesis is to construct a tensor product on the 2-category BFC-A of braided fusion categories containing a symmetric fusion category A. We achieve this by introducing the new notion of Z(A)-crossed braided categories. These are categories enriched over the Drinfeld centre Z(A) of the symmetric fusion category. We show that Z(A) admits an additional symmetric tensor structure, which makes it into a 2-fold monoidal category. ByTannaka duality, A= Rep(G) (or Rep(G; w)) for a finite group G (or finite super-group (G,w)). Under this identication Z(A) = VectG[G], the category of
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Stigner, Carl. "A classifying algebra for CFT boundary conditions." Licentiate thesis, Karlstad University, Faculty of Technology and Science, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-4890.

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<p>Conformal field theories (CFT) constitute an interesting class of twodimensionalquantum field theories, with applications in string theoryas well as condensed matter physics. The symmetries of a CFT can beencoded in the mathematical structure of a conformal vertex algebra.The rational CFT’s are distinguished by the property that the categoryof representations of the vertex algebra is a modular tensor category.The solution of a rational CFT can be split off into two separate tasks, apurely complex analytic and a purely algebraic part.</p><p>The TFT-construction gives a solution to the second
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Lallouche, Mickaël. "Théories des champs quantiques topologiques internes de type Reshetikhin-Turaev." Thesis, Montpellier, 2016. http://www.theses.fr/2016MONTS015/document.

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Une théorie des champs quantique topologique (TQFT) en dimension 3 est un foncteur monoidal symétrique de la catégorie des cobordismes de dimension 3 vers celle des espaces vectoriels. Une TQFT fournit en particulier un invariant scalaire des variétés fermées de dimension 3 ainsi que des représentations du groupe de difféotopie des surfaces fermées.Turaev explique en 1994 comment construire à partir d'une catégorie modulaire une TQFT qui étend l'invariant scalaire de 3-variétés fermées introduit en 1991 par Reshetikhin et Turaev. Dans cette thèse, nous généralisons cette construction à l'aide
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De, Renzi Marco. "Construction of extended topological quantum field theories." Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCC114/document.

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La position centrale occupée par les Théories Quantiques des Champs Topologiques (TQFTs) dans l’étude de la topologie en basse dimension est due à leur structure extraordinairement riche, qui permet différentes interactions et applications à des questions de nature géométrique. Depuis leur première apparition, un grand effort a été mis dans l’extension des invariants quantiques de 3-variétés en TQFTs et en TQFT Étendues (ETQFTs). Cette thèse s’attaque à ce problème dans deux cadres généraux différents. Le premier est l’étude des invariants quantiques semi-simples de Witten, Reshetikhin et Tura
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Books on the topic "Modular categories"

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1958-, Shelton Brad, ed. Categories of highest weight modules: Applications to classical Hermitian symmetric pairs. American Mathematical Society, 1987.

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W, Anderson Frank. Rings and categories of modules. 2nd ed. Springer-Verlag, 1992.

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Anderson, Frank W., and Kent R. Fuller. Rings and Categories of Modules. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-4418-9.

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Categories of modules over endomorphism rings. American Mathematical Society, 1993.

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Blecher, David P. Categories of operator modules: Morita equivalence and projective modules. American Mathematical Society, 2000.

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Zelmanowitz, Julius Martin. Duality for module categories. Verlag Reinhard Fischer, 1988.

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service), SpringerLink (Online, ed. Modules over operads and functors. Springer, 2009.

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Facchini, Alberto, Lorna Gregory, Sonia L’Innocente, and Marcus Tressl, eds. Model Theory of Modules, Algebras and Categories. American Mathematical Society, 2019. http://dx.doi.org/10.1090/conm/730.

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1941-, Keating M. E., ed. Categories and modules with K-theory in view. Cambridge University Press, 2000.

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Facchini, Alberto. Semilocal Categories and Modules with Semilocal Endomorphism Rings. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23284-9.

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Book chapters on the topic "Modular categories"

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Thiébaud, Michel. "Modular categories." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0084233.

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Bakalov, Bojko, and Alexander Kirillov. "Modular tensor categories." In Lectures on Tensor Categories and Modular Functors. American Mathematical Society, 2000. http://dx.doi.org/10.1090/ulect/021/04.

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Bakalov, Bojko, and Alexander Kirillov. "Modular functors." In Lectures on Tensor Categories and Modular Functors. American Mathematical Society, 2000. http://dx.doi.org/10.1090/ulect/021/06.

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Bakalov, Bojko, and Alexander Kirillov. "Moduli spaces and complex modular functors." In Lectures on Tensor Categories and Modular Functors. American Mathematical Society, 2000. http://dx.doi.org/10.1090/ulect/021/07.

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Bakalov, Bojko, and Alexander Kirillov. "Ribbon categories." In Lectures on Tensor Categories and Modular Functors. American Mathematical Society, 2000. http://dx.doi.org/10.1090/ulect/021/03.

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Andersen, Henning Haahr. "Quotient Categories of Modular Representations." In Representation Theory of Algebraic Groups and Quantum Groups. Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4697-4_1.

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Bakalov, Bojko, and Alexander Kirillov. "Braided tensor categories." In Lectures on Tensor Categories and Modular Functors. American Mathematical Society, 2000. http://dx.doi.org/10.1090/ulect/021/02.

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Blanchet, Christian, and Marco De Renzi. "Modular categories and TQFTs beyond semisimplicity." In Topology and Geometry. European Mathematical Society Publishing House, 2021. http://dx.doi.org/10.4171/irma/33-1/11.

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Müger, Michael. "The Modular Closure of Braided Tensor Categories." In Geometry and Quantum Physics. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-46552-9_19.

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Bakalov, Bojko, and Alexander Kirillov. "Introduction." In Lectures on Tensor Categories and Modular Functors. American Mathematical Society, 2000. http://dx.doi.org/10.1090/ulect/021/01.

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Conference papers on the topic "Modular categories"

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BLANCHET, CHRISTIAN. "INTRODUCTION TO QUANTUM INVARIANTS OF 3-MANIFOLDS, TOPOLOGICAL QUANTUM FIELD THEORIES AND MODULAR CATEGORIES." In Proceedings of the Summer School. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705068_0004.

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Snook, Kelly, Tarik Barri, Joachim Goßmann, Jason Potts, Margaret Schedel, and Hartmut Warm. "Kepler Concordia: Designing an Immersive Modular Musical and Scientific Instrument Using Novel Blockchain and Sonification Technologies in XR." In The 24th International Conference on Auditory Display. The International Community for Auditory Display, 2018. http://dx.doi.org/10.21785/icad2018.034.

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This paper describes the first steps in the creation of a new scientific and musical instrument to be released in 2019 for the 400th anniversary of Johannes Kepler's Harmonies of the World, which laid out his three laws of planetary motion and launched the field of modern astronomy. Concordia is a musical instrument that is modularly extensible, with its first software and hardware modules and underlying framework under construction now. The instrument is being designed in an immersive extended-reality (XR) environment with scientifically accurate visualizations and datatransparent sonificatio
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Song, Bin, Zenzhi Li, Yintai Ao, Xuejian Xiao, Hong Zhou, and W. F. Lu. "A Configurable Module Based Technology for Complex Engineering Process Management Systems." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84957.

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An integrated end-to-end lifecycle engineering process management system is deemed critical to boost the manageability, efficiency and responsiveness of an engineering enterprise. The challenge lies in the realization of such a system that is flexible and scalable. To overcome the challenge, a configurable module based system technology is developed to simplify the realization of a complex process management system and to offer the system a high level of flexibility and scalability. The technology is based on the belief that a complex process management system can be built by a set of static a
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Dharia, Mehul A., Danny L. Levine, Roy D. Crowninshield, Eik Siggelkow, Dale A. Degroff, and Douglas H. Wentz. "Effectiveness of Trabecular Metal™ Acetabular Augment in Revision THR of Pelvis With Severe Acetabular Defect: A Finite Element Study." In ASME 2007 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2007. http://dx.doi.org/10.1115/sbc2007-176222.

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Osteolysis of the pelvis after total hip replacement (THR) can result in several types of bony defects within or around the acetabulum [1]. These defects are classified into various categories based on the extent and location of the host bone loss [2, 3]. A severe acetabular defect with at least 30% of bone loss and progressive amounts of superior rim deficiencies can be classified as a Paprosky type IIIA cavitary defect [4] (Figure 1-I). A significant amount of superior migration of the cup can be expected as the deficient acetabulum with nonsupportive superior dome will be unable to support
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ALB, ALINA. "SOME COREFLECTIVE CATEGORIES OF TOPOLOGICAL MODULES." In Proceedings of the International Conference on Algebras, Modules and Rings. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774552_0001.

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Parseliunas, Eimuntas, and Saulius Urbanas. "Features of Flexible E-Learning Modules Within Geographical Information Science for Vocational Training." In ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2008. http://dx.doi.org/10.1115/esda2008-59093.

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The main features and general structures of two distant learning modules within geographical information science for vocational training are presented in this paper. “European Level Developments of Flexible Learning Models within Geographical Information Science (GIS) for Vocational Training (E-GIS)” was a pilot project under the Leonardo de Vinci Community action Programme on vocational training, within Geographical Information Science (GIS), to be implemented over a three year period, 2002–05. The project will be continued in 2008–2009 under the abbreviation eGIS+. The main objectives of the
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Hoorelbeke, Jean-Michel, Joël Chupeau, Jean Loubrieu, Jean-Baptiste Poisson, and Richard Poisson. "The Research in France on Disposal Concepts for High Level and Long Lived Radioactive Waste in Deep Clay Formation." In ASME 2001 8th International Conference on Radioactive Waste Management and Environmental Remediation. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/icem2001-1292.

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Abstract The 15 year research on high level and long lived radioactive waste disposal in deep geological formations is being carried out by the ANDRA within the framework of the 1991 law. The status of the research program corresponds to the sinking of the shafts of the Meuse/Haute-Marne Underground Research Laboratory in an argilite layer. A set of preliminary concepts associated to this argillite layer has been studied to help address the issues raised by the feasibility analysis of a potential repository with respect to safety objectives. These concepts deal with transuranic no heat emittin
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Apostolidis, Asteris, Suresh Sampath, Panagiotis Laskaridis, and Riti Singh. "WebEngine: A Web-Based Gas Turbine Performance Simulation Tool." In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-95296.

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The WebEngine is a web-based gas turbine performance simulation tool. The main advantage from this approach is the ease-of-use as no local installation is required. A number of different user categories such as students, researchers, gas turbine operators etc. can immensely benefit from this tool. The WebEngine has been under development for two years and is strongly supported by various associated research work in the department. It offers a large number of simulation capabilities such as design point and off-design single runs/parametric analysis, engine library, engine model design, virtual
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Ha, Sungdo, and Emanuel Sachs. "Categories of process variables: robustness optimization, uniformity tuning, and mean adjustment." In Process Module Metrology, Control and Clustering, edited by Cecil J. Davis, Irving P. Herman, and Terry R. Turner. SPIE, 1992. http://dx.doi.org/10.1117/12.56636.

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Miao, Yunjie, Feng Gao, and Yong Zhang. "Gait Fitting Algorithms for Snake Robots With Binary Actuators." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70108.

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This paper introduces a new snake robot with binary actuators and mainly focuses on the simulations of various snake gaits. Three categories of fitting algorithms are proposed. They are 1) Fitting Algorithm of One Module; 2) Position-Fitting Algorithm of Multiple Modules; 3) Configuration-Fitting Algorithm of Multiple Modules. All the fitting algorithms and their fitting results are elaborated in simulations of lateral undulation, one of the most widely used snake gaits. As the best fitting algorithm for lateral undulation, Configuration-Fitting Algorithm of Four Modules is also applied to a s
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Reports on the topic "Modular categories"

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Bao, Jieyi, Xiaoqiang Hu, Cheng Peng, Yi Jiang, Shuo Li, and Tommy Nantung. Truck Traffic and Load Spectra of Indiana Roadways for the Mechanistic-Empirical Pavement Design Guide. Purdue University, 2020. http://dx.doi.org/10.5703/1288284317227.

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The Mechanistic-Empirical Pavement Design Guide (MEPDG) has been employed for pavement design by the Indiana Department of Transportation (INDOT) since 2009 and has generated efficient pavement designs with a lower cost. It has been demonstrated that the success of MEPDG implementation depends largely on a high level of accuracy associated with the information supplied as design inputs. Vehicular traffic loading is one of the key factors that may cause not only pavement structural failures, such as fatigue cracking and rutting, but also functional surface distresses, including friction and smo
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