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Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail). The examples, of current interest, are intended to clarify certain mathematical aspects and to show their usefulness in physical problems. The topics treated include the differential geometry of Lie groups, fiber bundles and connections, characteristic classes, index theorems, monopoles, instantons, extensions of Lie groups and algebras, some applications in supersymmetry, Chevalley-Eilenberg approach to Lie algebra cohomology, symplectic cohomology, jet-bundle approach to variational principles in mechanics, Wess-Zumino-Witten terms, infinite Lie algebras, the cohomological descent in mechanics and in gauge theories and anomalies. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics.
List of contents
Preface; 1. Lie groups, fibre bundles and Cartan calculus; 2. Connections and characteristic classes; 3. A first look at cohomology of groups and related topics; 4. An introduction to abstract group extension theory; 5. Cohomology groups of a group G and extensions by an abelian kernel; 6. Cohomology of Lie algebras; 7. Group extensions by non-abelian kernels; 8. Cohomology and Wess-Zumino terms: an introduction; 9. Infinite-dimensional Lie groups and algebras; 10. Gauge anomalies; List of symbols; References; Index.
Summary
Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail).
