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Non Semisimple Extended Topological Quantum Field Theories


Non Semisimple Extended Topological Quantum Field Theories
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Non Semisimple Extended Topological Quantum Field Theories


Non Semisimple Extended Topological Quantum Field Theories
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Author : Marco De Renzi
language : en
Publisher:
Release Date : 2022

Non Semisimple Extended Topological Quantum Field Theories written by Marco De Renzi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Electronic books categories.


"We develop the general theory for the construction of Extended Topological Quantum Field Theories (ETQFTs) associated with the Costantino-Geer-Patureau quantum invariants of closed 3-manifolds. In order to do so, we introduce relative modular categories, a class of ribbon categories which are modeled on representations of unrolled quantum groups, and which can be thought of as a non-semisimple analogue to modular categories. Our approach exploits a 2-categorical version of the universal construction introduced by Blanchet, Habegger, Masbaum, and Vogel. The 1+1+1-EQFTs thus obtained are realized by symmetric monoidal 2-functors which are defined over non-rigid 2-categories of admissible cobordisms decorated with colored ribbon graphs and cohomology classes, and which take values in 2- categories of complete graded linear categories. In particular, our construction extends the family of graded 2+1-TQFTs defined for the unrolled version of quantum sl2 by Blanchet, Costantino, Geer, and Patureau to a new family of graded ETQFTs. The non-semisimplicity of the theory is witnessed by the presence of non-semisimple graded linear categories associated with critical 1-manifolds"--



Non Semisimple Extended Topological Quantum Field Theories


Non Semisimple Extended Topological Quantum Field Theories
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Author : Marco De Renzi
language : en
Publisher: American Mathematical Society
Release Date : 2022-05-24

Non Semisimple Extended Topological Quantum Field Theories written by Marco De Renzi and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-24 with Mathematics categories.


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Non Semisimple Topological Quantum Field Theories For 3 Manifolds With Corners


Non Semisimple Topological Quantum Field Theories For 3 Manifolds With Corners
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Author : Thomas Kerler
language : en
Publisher: Springer
Release Date : 2003-07-01

Non Semisimple Topological Quantum Field Theories For 3 Manifolds With Corners written by Thomas Kerler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Mathematics categories.


This book presents the (to date) most general approach to combinatorial constructions of topological quantum field theories (TQFTs) in three dimensions. The authors describe extended TQFTs as double functors between two naturally defined double categories: one of topological nature, made of 3-manifolds with corners, the other of algebraic nature, made of linear categories, functors, vector spaces and maps. Atiyah's conventional notion of TQFTs as well as the notion of modular functor from axiomatic conformal field theory are unified in this concept. A large class of such extended modular catergory is constructed, assigning a double functor to every abelian modular category, which does not have to be semisimple.



Non Semisimple Topological Quantum Field Theories For 3 Manifolds With Corners


Non Semisimple Topological Quantum Field Theories For 3 Manifolds With Corners
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Author : Thomas Kerler
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-09-11

Non Semisimple Topological Quantum Field Theories For 3 Manifolds With Corners written by Thomas Kerler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-11 with Mathematics categories.


This book presents the (to date) most general approach to combinatorial constructions of topological quantum field theories (TQFTs) in three dimensions. The authors describe extended TQFTs as double functors between two naturally defined double categories: one of topological nature, made of 3-manifolds with corners, the other of algebraic nature, made of linear categories, functors, vector spaces and maps. Atiyah's conventional notion of TQFTs as well as the notion of modular functor from axiomatic conformal field theory are unified in this concept. A large class of such extended modular catergory is constructed, assigning a double functor to every abelian modular category, which does not have to be semisimple.



Affine Hecke Algebras And Quantum Symmetric Pairs


Affine Hecke Algebras And Quantum Symmetric Pairs
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Author : Zhaobing Fan
language : en
Publisher: American Mathematical Society
Release Date : 2023-01-18

Affine Hecke Algebras And Quantum Symmetric Pairs written by Zhaobing Fan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-18 with Mathematics categories.


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Categories And Representation Theory


Categories And Representation Theory
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Author : Hideto Asashiba
language : en
Publisher: American Mathematical Society
Release Date : 2022-09-29

Categories And Representation Theory written by Hideto Asashiba and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-29 with Mathematics categories.


This book gives a self-contained account of applications of category theory to the theory of representations of algebras. Its main focus is on 2-categorical techniques, including 2-categorical covering theory. The book has few prerequisites beyond linear algebra and elementary ring theory, but familiarity with the basics of representations of quivers and of category theory will be helpful. In addition to providing an introduction to category theory, the book develops useful tools such as quivers, adjoints, string diagrams, and tensor products over a small category; gives an exposition of new advances such as a 2-categorical generalization of Cohen-Montgomery duality in pseudo-actions of a group; and develops the moderation level of categories, first proposed by Levy, to avoid the set theoretic paradox in category theory. The book is accessible to advanced undergraduate and graduate students who would like to study the representation theory of algebras, and it contains many exercises. It can be used as the textbook for an introductory course on the category theoretic approach with an emphasis on 2-categories, and as a reference for researchers in algebra interested in derived equivalences and covering theory.



Multi Parameter Hardy Spaces Theory And Endpoint Estimates For Multi Parameter Singular Integrals


Multi Parameter Hardy Spaces Theory And Endpoint Estimates For Multi Parameter Singular Integrals
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Author : Guozhen Lu
language : en
Publisher: American Mathematical Society
Release Date : 2023-01-18

Multi Parameter Hardy Spaces Theory And Endpoint Estimates For Multi Parameter Singular Integrals written by Guozhen Lu and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-18 with Mathematics categories.


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The Second Moment Theory Of Families Of L Functions The Case Of Twisted Hecke L Functions


The Second Moment Theory Of Families Of L Functions The Case Of Twisted Hecke L Functions
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Author : Valentin Blomer
language : en
Publisher: American Mathematical Society
Release Date : 2023-02-13

The Second Moment Theory Of Families Of L Functions The Case Of Twisted Hecke L Functions written by Valentin Blomer and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-13 with Mathematics categories.


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Hypergeometric Functions Over Finite Fields


Hypergeometric Functions Over Finite Fields
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Author : Jenny Fuselier
language : en
Publisher: American Mathematical Society
Release Date : 2022-11-10

Hypergeometric Functions Over Finite Fields written by Jenny Fuselier and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-10 with Mathematics categories.


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Planar Algebras In Braided Tensor Categories


Planar Algebras In Braided Tensor Categories
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Author : André Gil Henriques
language : en
Publisher: American Mathematical Society
Release Date : 2023-02-13

Planar Algebras In Braided Tensor Categories written by André Gil Henriques and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-13 with Mathematics categories.


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