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Relevant bibliographies by topics / Modular tensor categories

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Academic literature on the topic 'Modular tensor categories'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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Journal articles on the topic "Modular tensor categories"

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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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Rowell, Eric, Richard Stong, and Zhenghan Wang. "On Classification of Modular Tensor Categories." Communications in Mathematical Physics 292, no. 2 (2009): 343–89. http://dx.doi.org/10.1007/s00220-009-0908-z.

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Liu, Zhengwei, and Feng Xu. "Jones-Wassermann subfactors for modular tensor categories." Advances in Mathematics 355 (October 2019): 106775. http://dx.doi.org/10.1016/j.aim.2019.106775.

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Giorgetti, Luca, and Karl-Henning Rehren. "Bantay's trace in unitary modular tensor categories." Advances in Mathematics 319 (October 2017): 211–23. http://dx.doi.org/10.1016/j.aim.2017.08.018.

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Creutzig, Thomas, and Terry Gannon. "Logarithmic conformal field theory, log-modular tensor categories and modular forms." Journal of Physics A: Mathematical and Theoretical 50, no. 40 (2017): 404004. http://dx.doi.org/10.1088/1751-8121/aa8538.

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Kirillov, Alexander A. "On an inner product in modular tensor categories." Journal of the American Mathematical Society 9, no. 4 (1996): 1135–69. http://dx.doi.org/10.1090/s0894-0347-96-00210-x.

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Edie-Michell, Cain. "Simple current auto-equivalences of modular tensor categories." Proceedings of the American Mathematical Society 148, no. 4 (2019): 1415–28. http://dx.doi.org/10.1090/proc/14795.

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Kong, Liang, and Ingo Runkel. "Morita classes of algebras in modular tensor categories." Advances in Mathematics 219, no. 5 (2008): 1548–76. http://dx.doi.org/10.1016/j.aim.2008.07.004.

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Al-Shomrani, M. M., and E. J. Beggs. "Making nontrivially associated modular categories from finite groups." International Journal of Mathematics and Mathematical Sciences 2004, no. 42 (2004): 2231–64. http://dx.doi.org/10.1155/s0161171204308203.

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We show that the double𝒟of the nontrivially associated tensor category constructed from left coset representatives of a subgroup of a finite groupXis a modular category. Also we give a definition of the character of an object in this category as an element of a braided Hopf algebra in the category. This definition is shown to be adjoint invariant and multiplicative on tensor products. A detailed example is given. Finally, we show an equivalence of categories between the nontrivially associated double𝒟and the trivially associated category of representations of the Drinfeld double of the groupD(

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Dissertations / Theses on the topic "Modular tensor categories"

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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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Vieira, Larissa Hagedorn. "PARES ADMISSÍVEIS, SISTEMAS ADMISSÍVEIS E BIÁLGEBRAS NA CATEGORIA DOS MÓDULOS DE YETTER-DRINFELD." Universidade Federal de Santa Maria, 2014. http://repositorio.ufsm.br/handle/1/9989.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The purpose of this work is to study the relationships between admissible pairs, systems admissible and bialgebras in the category of Yetter-Drinfeld modules, as well as some properties of the Hopf algebra associated (via bosonization) to an admissible pair. We end this dissertation with a family of examples of admissible pairs.<br>O objetivo deste trabalho é estudar as relações entre pares admissíveis, sistemas admissíveis e biálgebras na categoria dos módulos de Yetter-Drinfeld, bem como algumas propriedades da álgebra de Hopf as

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Stirling, Spencer. "Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories." 2008. http://hdl.handle.net/2152/17795.

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Classical and quantum Chern-Simons with gauge group U(1)N were classified by Belov and Moore in [BM05]. They studied both ordinary topological quantum field theories as well as spin theories. On the other hand a correspondence is well known between ordinary (2 + 1)-dimensional TQFTs and modular tensor categories. We study group categories and extend them slightly to produce modular tensor categories that correspond to toral Chern-Simons. Group categories have been widely studied in other contexts in the literature [FK93],[Qui99],[JS93],[ENO05],[DGNO07]. The main result is a proof that the asso

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Giorgetti, Luca. "Braided Actions of DHR Categories and Reconstruction of Chiral Conformal Field Theories." Doctoral thesis, 2016. http://hdl.handle.net/11858/00-1735-0000-002B-7C2E-0.

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Books on the topic "Modular tensor categories"

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Bakalov, Bojko, and Alexander Kirillov. Lectures on Tensor Categories and Modular Functors (University Lecture Series). American Mathematical Society, 2000.

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de Villiers, Jill, and Tom Roeper. The Acquisition of Complements. Edited by Jeffrey L. Lidz, William Snyder, and Joe Pater. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780199601264.013.13.

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The development of complementation engages high-level parametric variation, a variety of separate modules, and very specific lexical variation across the possible grammars in UG. In particular, finiteness, argument structure, control, empty categories, and recursion all present separate challenges and create an intricate grammatical acquisition path for any child. The essential question is: how does the CP node expand from small clauses to infinitives to tensed clauses? The next question is: how does the grammar interface with cognition, as complements express propositional attitudes, and fals

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Book chapters on the topic "Modular tensor categories"

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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. "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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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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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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Bakalov, Bojko, and Alexander Kirillov. "3-dimensional topological quantum field theory." In Lectures on Tensor Categories and Modular Functors. American Mathematical Society, 2000. http://dx.doi.org/10.1090/ulect/021/05.

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Bakalov, Bojko, and Alexander Kirillov. "Wess-Zumino-Witten model." In Lectures on Tensor Categories and Modular Functors. American Mathematical Society, 2000. http://dx.doi.org/10.1090/ulect/021/08.

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Bischoff, Marcel, Yasuyuki Kawahigashi, Roberto Longo, and Karl-Henning Rehren. "Frobenius Algebras, Q-Systems and Modules." In Tensor Categories and Endomorphisms of von Neumann Algebras. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14301-9_3.

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Conference papers on the topic "Modular tensor categories"

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Cohen, Eliad, Vishesh Vikas, Barry Trimmer, and Stephen McCarthy. "Design Methodologies for Soft-Material Robots Through Additive Manufacturing, From Prototyping to Locomotion." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47507.

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Soft material robots have gained interest in recent years due to the mechanical potential of non-rigid materials and technological development in the additive manufacturing (3D printing) techniques. The incorporation of soft materials provides robots with potential for locomotion in unstructured environments due to the conformability and deformability properties of the structure. Current additive manufacturing techniques allow multimaterial printing which can be utilized to build soft bodied robots with rigid-material inclusions/features in a single process, single batch (low manufacturing vol

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Kim, Jin Sung, Hyun Seung Jung, Tae Soo Kwon, Won Mok Choi, and Seung Wan Son. "Full-Scale Crash Testing Facilities for a Railway Vehicle." In 2012 Joint Rail Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/jrc2012-74009.

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KRRI (Korea Railroad Research Institute) has successfully performed several tens of impact tests of crash parts for a railway vehicles. Full-scale crash testing facilities were newly established including a crash barrier, dynamic load cell, high speed DAS (Data Acquisition System), a laser displacement sensor, dummies, a motor car and etc. This paper introduces series of impact test results using full-scale crash testing facilities. The impact test for railway vehicles consists of three categories, i.e. single item tests, module tests and crash structure tests. For single item tests, expansion

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