Quantum symmetries on operator algebras
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Bibliographic Information
Quantum symmetries on operator algebras
（Oxford mathematical monographs）
Clarendon Press, 1998
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Includes bibliography (p. [765]-818) and index
Description and Table of Contents
Description
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 algebras, quantum groups, low dimensional topology) and mathematical physics (integrable theories, statistical mechanics, conformal field theories and the string theories
of elementary particles). The theory of operator algebras was initiated by von Neumann and Murray as a tool for studying group representations and as a framework for quantum mechanics, and has since kept in touch with its roots in physics as a framework for quantum statistical mechanics and the formalism of
algebraic quantum field theory. However, in 1981, the study of operator algebras took a new turn with the introduction by Vaughan Jones of subfactor theory and remarkable connections were found with knot theory, 3-manifolds, quantum groups and integrable systems in statistical mechanics and conformal field theory. The purpose of this book, one of the first in the area, is to look at these combinatorial-algebraic developments from the perspective of operator algebras; to bring the reader to
the frontline of research with the minimum of prerequisites from classical theory.
Table of Contents
- 1. Operator theory basics
- 2. C*-algebra basics
- 3. K-theory
- 4. Positivity and semigroups
- 5. von Neumann algebra basics
- 6. The Fermion algebra
- 7. The Ising model
- 8. Conformal field theory
- 9. Subfactors and bimodules
- 10. Axiomatization of paragroups
- 11. String algebras and flat connections
- 12. Topological quantum field theory (TQFT) and paragroups
- 13. Rational conformal field theory (RCFT) and paragroups
- 14. Commuting squares of II1 factors
- 15. Automorphisms of subfactors and central sequences
- Bibliography
- Index
by "Nielsen BookData"