Journal ArticleDOI
On Galois theory from subfactors
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TLDR
In this article, it was shown that the fixed point group-subgroup subfactor N G ⊆ N H is conjugate to the group subfactor n G / H ⊈ N.Abstract:
We review some concepts of Galois theory for subfactors N ⊆ M , computing some Galois groups and correspondences in this framework. Given an outer action of a group G on a II 1 von Neumann factor N and a normal subgroup H of G, we prove that the fixed point group–subgroup subfactor N G ⊆ N H is conjugate to the group–subfactor N G / H ⊆ N .read more
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Book
Conformal Field Theory
TL;DR: This paper developed conformal field theory from first principles and provided a self-contained, pedagogical, and exhaustive treatment, including a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algesas.
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Quantum symmetries on operator algebras
David Evans,Yasuyuki Kawahigashi +1 more
TL;DR: In the last 20 years, the study of operator algebras has developed from a branch of functional analysis to a central field of mathematics with applications and connections with different areas in both pure mathematics (foliations, index theory, K-theory, cyclic homology, affine Kac--Moody algesbras, quantum groups, low dimensional topology) and mathematical physics (integrable theories, statistical mechanics, conformal field theories and the string theories of elementary particles).
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An axiomatization of the lattice of higher relative commutants of a subfactor
TL;DR: In this paper, the authors consider certain conditions for abstract lattices of commuting squares, that they prove are necessary and sufficient for them to arise as lattices with higher relative commutants of a subfactor.
Journal ArticleDOI
A Galois Correspondence for Compact Groups of Automorphisms of von Neumann Algebras with a Generalization to Kac Algebras
TL;DR: In this paper, a factor with separable predual and Ga compact group of automorphisms whose action is minimal is defined, i.e., MG ∩M=C, where MG denotes the G-fixed point subalgebra.