2022-05-23T00:00:26Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000219662021-09-02T06:32:36Z1169:1170The Batalin-Vilkovisky Algebra in the String Topology of Classifying SpacesKuribayashi, KatsuhikoMenichi, Lucstring topologyBatalin-Vilkovisky algebraclassifying spaceFor almost any compact connected Lie group C and any field F-p, we compute the Batalin-Vilkovisky algebra H*(+dim G) (LBG; F-p) on the loop cohomology of the classifying space introduced by Chataur and the second author. In particular, if p is odd or p = 0, this Batalin-Vilkovisky algebra is isomorphic to the Hochschild cohomology HH* (H-*(G), H-* (G)). Over F-2, such an isomorphism of Batalin-Vilkovisky algebras does not hold when G = SO(3) or G = G(2). Our elaborate considerations on the signs in string topology of the classifying spaces give rise to a general theorem on graded homological conformal field theory.ArticleCANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES.71(4):843-889(2019)journal articleCAMBRIDGE UNIV PRESS2019-01-09application/pdfCANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES4718438890008-414XAA00597678https://soar-ir.repo.nii.ac.jp/record/21966/files/16K13753_01.pdfeng10.4153/CJM-2018-021-9https://doi.org/10.4153/CJM-2018-021-9This article has been published in a revised form in CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, https://doi.org/10.4153/CJM-2018-021-9. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © Canadian Mathematical Society 2018.