Christoph Schweigert's Books

Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I

By: Simon Lentner,Svea Nora Mierach,Christoph Schweigert,Yorck Sommerhäuser

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Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I

By: Simon Lentner,Svea Nora Mierach,Christoph Schweigert,Yorck Sommerhäuser

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 their mapping class groups. Thereafter, it explains how representations of these groups are constructed in topological field theory, using an approach via nets and ribbon graphs. These tools are then used to show that the mapping class groups indeed act on the so-called derived block spaces. Toward the end, the book explains the relation to Hochschild cohomology of Hopf algebras and the modular group.

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Springer Nature

Published Date

ISBN 10

9811946450

ISBN 13

9789811946455

Symmetries, Lie Algebras and Representations

A Graduate Course for Physicists

By: Jürgen Fuchs,Christoph Schweigert

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Symmetries, Lie Algebras and Representations

A Graduate Course for Physicists

By: Jürgen Fuchs,Christoph Schweigert

This book gives an introduction to Lie algebras and their representations. Lie algebras have many applications in mathematics and physics, and any physicist or applied mathematician must nowadays be well acquainted with them.

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Page Count

464

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Cambridge University Press

Published Date

ISBN 10

0521541190

ISBN 13

9780521541190

String-Net Construction of RCFT Correlators

By: Jürgen Fuchs,Christoph Schweigert,Yang Yang

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String-Net Construction of RCFT Correlators

By: Jürgen Fuchs,Christoph Schweigert,Yang Yang

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 invariants under appropriate mapping class groups that are compatible with factorization. The authors extract operator products of field objects from specific correlators; the resulting operator products are natural algebraic expressions that make sense beyond semisimplicity. They also derive an Eckmann-Hilton relation internal to a braided category, thereby demonstrating the utility of string nets for understanding algebra in braided tensor categories. Finally, they introduce the notion of a universal correlator. This systematizes the treatment of situations in which different world sheets have the same correlator and allows for the definition of a more comprehensive mapping class group.

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Page Count

129

Publisher

Springer Nature

Published Date

ISBN 10

3031146824

ISBN 13

9783031146824

On power system automation:

A Digital Twin-centric framework for the next generation of energy management systems

By: Christoph Brosinsky

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On power system automation:

A Digital Twin-centric framework for the next generation of energy management systems

By: Christoph Brosinsky

The ubiquitous digital transformation also influences power system operation. Emerging real-time applications in information (IT) and operational technology (OT) provide new opportunities to address the increasingly demanding power system operation imposed by the progressing energy transition. This IT/OT convergence is epitomised by the novel Digital Twin (DT) concept. By integrating sensor data into analytical models and aligning the model states with the observed system, a power system DT can be created. As a result, a validated high-fidelity model is derived, which can be applied within the next generation of energy management systems (EMS) to support power system operation. By providing a consistent and maintainable data model, the modular DT-centric EMS proposed in this work addresses several key requirements of modern EMS architectures. It increases the situation awareness in the control room, enables the implementation of model maintenance routines, and facilitates automation approaches, while raising the confidence into operational decisions deduced from the validated model. This gain in trust contributes to the digital transformation and enables a higher degree of power system automation. By considering operational planning and power system operation processes, a direct link to practice is ensured. The feasibility of the concept is examined by numerical case studies.

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230

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BoD – Books on Demand

Published Date

ISBN 10

3863602668

ISBN 13

9783863602666

Symmetries, Lie Algebras and Representations

A Graduate Course for Physicists

By: Jürgen Fuchs,Christoph Schweigert

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Symmetries, Lie Algebras and Representations

A Graduate Course for Physicists

By: Jürgen Fuchs,Christoph Schweigert

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Page Count

464

Publisher

Cambridge University Press

Published Date

ISBN 10

0521541190

ISBN 13

9780521541190

Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I

By: Simon Lentner,Svea Nora Mierach,Christoph Schweigert,Yorck Sommerhäuser

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Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I

By: Simon Lentner,Svea Nora Mierach,Christoph Schweigert,Yorck Sommerhäuser

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Springer Nature

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ISBN 10

9811946450

ISBN 13

9789811946455

String-Net Construction of RCFT Correlators

By: Jürgen Fuchs,Christoph Schweigert,Yang Yang

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String-Net Construction of RCFT Correlators

By: Jürgen Fuchs,Christoph Schweigert,Yang Yang

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Solve jigsaw puzzle

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Page Count

129

Publisher

Springer Nature

Published Date

ISBN 10

3031146824

ISBN 13

9783031146824

Book's by Christoph Schweigert

Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I

Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I

Symmetries, Lie Algebras and Representations

Symmetries, Lie Algebras and Representations

String-Net Construction of RCFT Correlators

String-Net Construction of RCFT Correlators

On power system automation:

On power system automation:

Symmetries, Lie Algebras and Representations

Symmetries, Lie Algebras and Representations

Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I

Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I

String-Net Construction of RCFT Correlators

String-Net Construction of RCFT Correlators

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