W^*-Algebra A -algebra is a C-*-algebra for which there is a Banach space such that its dual is . Then the space is uniquely defined and is called the pre-dual of . Every von Neumann algebra is

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These are lecture notes from author's mini-course during Session 1: Vertex algebras, W-algebras, and application of INdAM Intensive research period Perspectives in Lie Theory, at the Centro

A W algebra is a higher spin extension of the Virasoro algebra. It is an extended symmetry algebra in conformal field theory. References 0.2 An early survey is Peter

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