Topological Quantum Field Theories from Subfactors

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A01=Vijay Kodiyalam
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Algebra
Ambient Isotopy
Author_Vijay Kodiyalam
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Basis
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Category=PHQ
Category=PHU
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Complex Group Algebra
Conjugacy Classes
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Coxeter Diagram
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Finite Dimensional Hilbert Space
finite-depth subfactors
Hilbert
Hilbert Space
Homotopic Rel
Hopf Algebra
Intertwiner Spaces
Irreducible Unitary Representations
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Neumann
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Orthonormal
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Perron Frobenius Eigenvalue
Perron Frobenius Eigenvector
Positive Functional
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Quantisation Functor
Quantum Double
Sesquilinear Form
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Space
Topological Quantum Field Theories
Total
Turaev-Viro construction
Vertex Set
Von
Von Neumann Algebras

Product details

  • ISBN 9781138442108
  • Weight: 410g
  • Dimensions: 156 x 234mm
  • Publication Date: 30 Sep 2020
  • Publisher: Taylor & Francis Ltd
  • Publication City/Country: GB
  • Product Form: Hardback
  • Language: English
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Pure mathematicians have only recently begun a rigorous study of topological quantum field theories (TQFTs). Ocneanu, in particular, showed that subfactors yield TQFTs that complement the Turaev-Viro construction. Until now, however, it has been difficult to find an account of this work that is both detailed and accessible. Topological Quantum Field Theories from Subfactors provides a self-contained, explicit description of Ocneanu's construction It introduces and discusses its various ingredients with the distinct advantage of employing only genuine triangulations. The authors begin with axioms for a TQFT, go through the Turaev-Viro prescription for constructing such a TQFT, and finally work through Ocneanu's method of starting with a finite depth hyperfinite subfactor" and obtaining the data needed to invoke the Turaev-Viro machine. The authors provide a very concise treatment of finite factors of type and their bimodules and include details and calculations for all constructions. They also present, perhaps for the first time in book form, notions such as quantization functors and fusion algebras. Accessible to graduate students and others just beginning to explore this intriguing topic, Topological Quantum Field Theories from Subfactors will also be of interest to researchers in both mathematics and theoretical physics.
Kodiyalam, Vijay