| 书目名称 | Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I | | 编辑 | Simon Lentner,Svea Nora Mierach,Yorck Sommerhäuser | | 视频video | | | 概述 | Discusses conformal field theory in a non-semisimple setting.Uses Lyubashenko’s approach via nets and ribbon graphs.Describes the relation to Hochschild cohomology of Hopf algebras | | 丛书名称 | SpringerBriefs in Mathematical Physics | | 图书封面 |  | | 描述 | 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.. | | 出版日期 | Book 2023 | | 关键词 | modular tensor category; Hochschild Cohomology; Hopf algebra; modular group; the Birman sequence | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-19-4645-5 | | isbn_softcover | 978-981-19-4644-8 | | isbn_ebook | 978-981-19-4645-5Series ISSN 2197-1757 Series E-ISSN 2197-1765 | | issn_series | 2197-1757 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor |
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发表于 2025-3-21 16:12:45
