Dualizable Tensor Categories
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Dualizable Tensor Categories
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Author : Christopher L. Douglas
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18
Dualizable Tensor Categories written by Christopher L. Douglas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Education categories.
We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with cer-tain algebraic properties determine topological invariants. We prove that fusion categories of nonzero global dimension are 3-dualizable, and therefore provide 3-dimensional 3-framed local field theories. We also show that all finite tensor cat-egories are 2-dualizable, and yield categorified 2-dimensional 3-framed local field theories. On the other hand, topological properties of 3-framed manifolds deter-mine algebraic equations among functors of tensor categories. We show that the 1-dimensional loop bordism, which exhibits a single full rotation, acts as the double dual autofunctor of a tensor category. We prove that the 2-dimensional belt-trick bordism, which unravels a double rotation, operates on any finite tensor category, and therefore supplies a trivialization of the quadruple dual. This approach pro-duces a quadruple-dual theorem for suitably dualizable objects in any symmetric monoidal 3-category. There is furthermore a correspondence between algebraic structures on tensor categories and homotopy fixed point structures, which in turn provide structured field theories; we describe the expected connection between piv-otal tensor categories and combed fixed point structures, and between spherical tensor categories and oriented fixed point structures.
Tensor Categories
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Author : Pavel Etingof
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-08-05
Tensor Categories written by Pavel Etingof and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Mathematics categories.
Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Decoupling On The Wiener Space Related Besov Spaces And Applications To Bsdes
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Author : Stefan Geiss
language : en
Publisher: American Mathematical Society
Release Date : 2021-11-16
Decoupling On The Wiener Space Related Besov Spaces And Applications To Bsdes written by Stefan Geiss 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 2021-11-16 with Mathematics categories.
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Instability Index Theorem And Exponential Trichotomy For Linear Hamiltonian Pdes
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Author : Zhiwu Lin
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-02
Instability Index Theorem And Exponential Trichotomy For Linear Hamiltonian Pdes written by Zhiwu Lin 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 2022-02-02 with Mathematics categories.
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Cell Complexes Poset Topology And The Representation Theory Of Algebras Arising In Algebraic Combinatorics And Discrete Geometry
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Author : Stuart Margolis
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-30
Cell Complexes Poset Topology And The Representation Theory Of Algebras Arising In Algebraic Combinatorics And Discrete Geometry written by Stuart Margolis 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 2021-12-30 with Mathematics categories.
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The Yang Mills Heat Equation With Finite Action In Three Dimensions
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Author : Leonard Gross
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-02
The Yang Mills Heat Equation With Finite Action In Three Dimensions written by Leonard Gross 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 2022-02-02 with Mathematics categories.
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Naturality And Mapping Class Groups In Heegard Floer Homology
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Author : András Juhász
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-09
Naturality And Mapping Class Groups In Heegard Floer Homology written by András Juhász 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 2021-12-09 with Mathematics categories.
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The Brunn Minkowski Inequality And A Minkowski Problem For Nonlinear Capacity
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Author : Murat Akman
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-02
The Brunn Minkowski Inequality And A Minkowski Problem For Nonlinear Capacity written by Murat Akman 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 2022-02-02 with Mathematics categories.
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Ergodicity Of Markov Processes Via Nonstandard Analysis
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Author : Haosui Duanmu
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-09
Ergodicity Of Markov Processes Via Nonstandard Analysis written by Haosui Duanmu 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 2021-12-09 with Mathematics categories.
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Tits Polygons
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Author : Bernhard Mühlherr
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-02
Tits Polygons written by Bernhard Mühlherr 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 2022-02-02 with Mathematics categories.
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