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Higher genus mapping class group invariants from factorizable Hopf algebras
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.ORCID iD: 0000-0003-4081-6234
Hamburg University.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.
2014 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 250, 285-319 p.Article in journal (Refereed) Published
Abstract [en]

Lyubashenko's construction associates representations of mapping class groups Map_{g,n} of Riemann surfaces of any genus g with any number n of holes to a factorizable ribbon category. We consider this construction as applied to the category of bimodules over a finite-dimensional factorizable ribbon Hopf algebra H. For any such Hopf algebra we find an invariant of Map_{g,n} for all values of g and n. More generally, we obtain such invariants for any pair (H,omega), where omega is a ribbon automorphism of H. Our results are motivated by the quest to understand correlation functions of bulk fields in two-dimensional conformal field theories with chiral algebras that are not necessarily semisimple, so-called logarithmic conformal field theories.

Place, publisher, year, edition, pages
Elsevier, 2014. Vol. 250, 285-319 p.
Keyword [en]
Factorizable Hopf algebras; Mapping class groups; Modular invariant partition functions
National Category
Other Mathematics
Research subject
Physics; Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-30285DOI: 10.1016/j.aim.2013.09.019ISI: 000327000400009OAI: oai:DiVA.org:kau-30285DiVA: diva2:667545
Available from: 2013-11-26 Created: 2013-11-26 Last updated: 2015-12-29Bibliographically approved

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Publisher's full texthttp://www.sciencedirect.com/science/article/pii/S0001870813003563http://xxx.lanl.gov/abs/1207.6863

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