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＜電子ブック＞
Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I / by Simon Lentner, Svea Nora Mierach, Christoph Schweigert, Yorck Sommerhäuser
(SpringerBriefs in Mathematical Physics. ISSN:21971765 ; 44)

版	1st ed. 2023.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2023
本文言語	英語
大きさ	IX, 68 p. 16 illus., 14 illus. in color : online resource
著者標目	*Lentner, Simon author Mierach, Svea Nora author Schweigert, Christoph author Sommerhäuser, Yorck author SpringerLink (Online service)
件　名	LCSH:Mathematical physics LCSH:Algebraic topology LCSH:Algebra, Homological FREE:Mathematical Physics FREE:Algebraic Topology FREE:Category Theory, Homological Algebra
一般注記	Mapping class groups -- Tensor categories -- Derived functors 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 HTTP:URL=https://doi.org/10.1007/978-981-19-4645-5

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