This is an introduction to Lie algebras and their applications in physics. The first three chapters show how Lie algebras arise naturally from symmetries of physical systems and illustrate through examples much of their general structure. Chapters 4 to 13 give a detailed introduction to Lie algebras and their representations, covering the Cartan-Weyl basis, simple and affine Lie algebras, real forms and Lie groups, the Weyl group, automorphisms, loop algebras and highest weight representations. Chapters 14 to 22 cover specific further topics, such as Verma modules, Casimirs, tensor products...
This is an introduction to Lie algebras and their applications in physics. The first three chapters show how Lie algebras arise naturally from symmetr...
Computeralgebra- Systeme wie MAPLE gehoren heute zum Alltag aller, die Mathematik in Schule, Wirtschaft und Hochschule anwenden. Gleichzeitig bieten sie die Moglichkeit, in ganz anderer Weise Beispiele zu untersuchen und zu veranschaulichen, als dies mit Bleistift und Papier moglich ist. Neben einer Einfuhrung in MAPLE hat dieses Buch zum Ziel, durch die Behandlung von Beispielen den Stoff des ersten Studienjahres, wie er in den Vorlesungen zur Analysis und Linearen Algebra behandelt wird, zu vertiefen und zu veranschaulichen. Es besteht aus Aufgaben mit Erlauterungen, anhand derer der Leser...
Computeralgebra- Systeme wie MAPLE gehoren heute zum Alltag aller, die Mathematik in Schule, Wirtschaft und Hochschule anwenden. Gleichzeitig bieten s...
This book studies using string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. The authors obtain concise geometric expressions for the objects describing bulk and boundary fields in terms of idempotents in the cylinder category of the underlying modular fusion category, comprising more general classes of fields than is standard in the literature. Combining these idempotents with Frobenius graphs on the world sheet yields string nets that form a consistent system of correlators, i.e. a system of...
This book studies using string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conforma...
Simon Lentner Svea Nora Mierach Christoph Schweigert
The book addresses a key question in topological field theory and logarithmic conformal field theory: In the case where the underlying modular category is not semisimple, topological field theory appears to suggest that mapping class groups do not only act on the spaces of chiral conformal blocks, which arise from the homomorphism functors in the category, but also act on the spaces that arise from the corresponding derived functors. It is natural to ask whether this is indeed the case. The book carefully approaches this question by first providing a detailed introduction to surfaces and...
The book addresses a key question in topological field theory and logarithmic conformal field theory: In the case where the underlying modular categor...
