Relevant bibliographies by topics / Tannaka duality

Academic literature on the topic 'Tannaka duality'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Tannaka duality"

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Bhatt, Bhargav, and Daniel Halpern-Leistner. "Tannaka duality revisited." Advances in Mathematics 316 (August 2017): 576–612. http://dx.doi.org/10.1016/j.aim.2016.08.040.

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Bhatt, Bhargav. "Algebraization and Tannaka duality." Cambridge Journal of Mathematics 4, no. 4 (2016): 403–61. http://dx.doi.org/10.4310/cjm.2016.v4.n4.a1.

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McCrudden, Paddy. "Tannaka duality for Maschkean categories." Journal of Pure and Applied Algebra 168, no. 2-3 (March 2002): 265–307. http://dx.doi.org/10.1016/s0022-4049(01)00099-8.

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Savin, Valentin. "Tannaka duality on quotient stacks." manuscripta mathematica 119, no. 3 (January 23, 2006): 287–303. http://dx.doi.org/10.1007/s00229-005-0616-8.

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Bui, Huu Hung. "Compact quantum groups and their corepresentations." Bulletin of the Australian Mathematical Society 57, no. 1 (February 1998): 73–91. http://dx.doi.org/10.1017/s0004972700031439.

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A compact quantum group is defined to be a unital Hopf C*–algebra generated by the matrix elements of a family of invertible corepresentations. We present a version of the Tannaka–Krein duality theorem for compact quantum groups in the context of abstract categories; this result encompasses the result of Woronowicz and the classical Tannaka-Krein duality theorem. We construct the orthogonality relations (similar to the case of compact groups). The Plancherel theorem is then established.
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Amini, Massoud. "Tannaka-Krein duality for compact groupoids II, duality." Operators and Matrices, no. 4 (2010): 573–92. http://dx.doi.org/10.7153/oam-04-32.

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Lu, Di-Ming. "TANNAKA DUALITY AND THE FRT-CONSTRUCTION." Communications in Algebra 29, no. 12 (January 1, 2001): 5717–31. http://dx.doi.org/10.1081/agb-100107955.

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Iwanari, Isamu. "Tannaka duality and stable infinity-categories." Journal of Topology 11, no. 2 (April 12, 2018): 469–526. http://dx.doi.org/10.1112/topo.12057.

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Hai, Phùng Hô. "Tannaka-Krein duality for Hopf algebroids." Israel Journal of Mathematics 167, no. 1 (October 2008): 193–225. http://dx.doi.org/10.1007/s11856-008-1047-5.

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Trentinaglia, Giorgio. "Tannaka duality for proper Lie groupoids." Journal of Pure and Applied Algebra 214, no. 6 (June 2010): 750–68. http://dx.doi.org/10.1016/j.jpaa.2009.08.004.

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Dissertations / Theses on the topic "Tannaka duality"

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Wallbridge, James. "Higher Tannaka duality." Toulouse 3, 2011. http://thesesups.ups-tlse.fr/1440/.

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Dans cette thèse, nous prouvons un théorème de dualité de Tannaka pour les (infini, 1)-catégories. La dualité classique de Tannaka est une dualité entre certains groupes et catégories monoïdales munies d'une structure particulière. La dualité de Tannaka supérieure renvoie, elle, à une dualité entre certains champs en groupes dérivés et certaines (infini, 1)-catégories monoïdales munies d'une structure particulière. Cette dualité supérieure est définie sur les anneaux dérivés et englobe la théorie de dualité classique. Nous comparons la dualité de Tannaka supérieure à la théorie de dualité de Tannaka classique et portons une attention particulière à la dualité de Tannaka sur les corps. Dans ce dernier cas, cette théorie a une relation étroite avec la théorie des types d'homotopie schématique de Toën. Nous décrivons également trois applications de la théorie : les complexes parfaits, les motifs et leur analogue non-commutatif dû à Kontsevich
In this thesis we prove a Tannaka duality theorem for (infini, 1)-categories. Classical Tannaka duality is a duality between certain groups and certain monoidal categories endowed with particular structure. Higher Tannaka duality refers to a duality between certain derived group stacks and certain monoidal (infini, 1)-categories endowed with particular structure. This higher duality theorem is defined over derived rings and subsumes the classical statement. We compare the higher Tannaka duality to the classical theory and pay particular attention to higher Tannaka duality over fields. In the later case this theory has a close relationship with the theory of schematic homotopy types of Toën. We also describe three applications of our theory : perfect complexes and that of both motives and its non-commutative ana­logue due to Kontsevich
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Rivezzi, Andrea. "Lie bialgebras and Etingof-Kazhdan quantization." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21784/.

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In questa tesi viene presentata la soluzione data da Pavel Etingof e David Kazhdan al problema della quantizzazione delle bialgebre di Lie, formulato da Vladimir Drinfeld nel 1992. Il problema consiste nel trovare un funtore che, data una bialgebra di Lie, costruisca una algebra di Hopf che la quantizzi. Nel primo capitolo vengono presentati gli aspetti di teoria delle categorie necessarie per la lettura. Nel secondo capitolo, introduciamo le nozioni di algebra, coalgebra, bialgebra e algebra di Hopf, con particolare attenzione alla loro teoria delle rappresentazioni. Nel terzo capitolo, presentiamo le nozioni base della teoria delle algebre di Lie, per poi definire le nozioni di coalgebra di Lie e di bialgebra di Lie. Vengono quindi definite le triple di Manin e il doppio di Drinfeld di una bialgebra di Lie. Nel quarto capitolo definiamo la nozione di quantizzazione di una bialgebra di Lie, e presentiamo i quantum groups di Drinfeld e Jimbo, che ne sono un esempio nel caso delle algebre di Kac-Moody simmetrizzabili. Infine, nel quinto ed ultimo capitolo presentiamo la costruzione della quantizzazione di Etingof e Kazhdan. Tale tecnica di quantizzazione si suddivide in diversi passi, ed è basata sulla dualità di Tannaka-Krein. In un primo momento, analizziamo il caso in cui la bialgebra di Lie è di dimensione finita. In seguito, adattiamo la costruzione del caso finito dimensionale al caso infinito dimensionale.
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Comeau, Marc A. "Premonoidal *-Categories and Algebraic Quantum Field Theory." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/22652.

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Algebraic Quantum Field Theory (AQFT) is a mathematically rigorous framework that was developed to model the interaction of quantum mechanics and relativity. In AQFT, quantum mechanics is modelled by C*-algebras of observables and relativity is usually modelled in Minkowski space. In this thesis we will consider a generalization of AQFT which was inspired by the work of Abramsky and Coecke on abstract quantum mechanics [1, 2]. In their work, Abramsky and Coecke develop a categorical framework that captures many of the essential features of finite-dimensional quantum mechanics. In our setting we develop a categorified version of AQFT, which we call premonoidal C*-quantum field theory, and in the process we establish many analogues of classical results from AQFT. Along the way we also exhibit a number of new concepts, such as a von Neumann category, and prove several properties they possess. We also establish some results that could lead to proving a premonoidal version of the classical Doplicher-Roberts theorem, and conjecture a possible solution to constructing a fibre-functor. Lastly we look at two variations on AQFT in which a causal order on double cones in Minkowski space is considered.
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Wallbridge, James. "Higher Tannaka duality." Thesis, 2011. http://hdl.handle.net/2440/69436.

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In this thesis we prove a Tannaka duality theorem for (∞, 1)-categories. Classical Tannaka duality is a duality between certain groups and certain monoidal categories endowed with particular structure. Higher Tannaka duality refers to a duality between certain derived group stacks and certain monoidal (∞, 1)-categories endowed with particular structure. This higher duality theorem is defined over derived rings and subsumes the classical statement. We compare the higher Tannaka duality to the classical theory and pay particular attention to higher Tannaka duality over fields. In the later case this theory has a close relationship with the theory of schematic homotopy types of Toёn. We also describe three applications of our theory: perfect complexes and that of both motives and its non-commutative analogue due to Kontsevich.
Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2011
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Book chapters on the topic "Tannaka duality"

1

Joyal, André, and Ross Street. "An introduction to Tannaka duality and quantum groups." In Lecture Notes in Mathematics, 413–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0084235.

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Banica, Teo. "Tannakian Duality." In Introduction to Quantum Groups, 81–106. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-23817-8_4.

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"Tannaka duality without schemes." In Graduate Studies in Mathematics, 243–53. Providence, Rhode Island: American Mathematical Society, 2016. http://dx.doi.org/10.1090/gsm/177/21.

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