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Vertex Operator Algebras
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Introduction to Operator Algebras - PDF Free Download
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Lecture 1. Introduction to von Neumann algebras.
Syllabus and other Information
Definition and examples. Von Neumann density theorem.
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Tomita-Takesaki theory and Connes decomposition and classification. Lecture 2.
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Subfactors and elementary examples. Index in the type II case. The tower of relative commutants and restrictions on index values. Construction of examples. Braid group representations and knot polynomials.
Lecture 3. Kauffman diagrams for the Temperley-Lieb algebra. Planar algebras, lambda lattices - the standard invariant of a subfactor and reconstruction. Random matrices with a real number of matrices.