Klein Topological Field Theories from Group Representations

We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in this theory with the Frobenius-Schur indicator on the represe...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2011
Автори: Loktev, S.A., Natanzon, S.M.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2011
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/147393
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Klein Topological Field Theories from Group Representations / S.A. Loktev, S.M. Natanzon // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Loktev, S.A.
Natanzon, S.M.
author_facet Loktev, S.A.
Natanzon, S.M.
citation_txt Klein Topological Field Theories from Group Representations / S.A. Loktev, S.M. Natanzon // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in this theory with the Frobenius-Schur indicator on the representation. We relate any complex simple Klein TFT to a real division ring.
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spelling Loktev, S.A.
Natanzon, S.M.
2019-02-14T17:24:55Z
2019-02-14T17:24:55Z
2011
Klein Topological Field Theories from Group Representations / S.A. Loktev, S.M. Natanzon // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 57R56; 20C05
DOI:10.3842/SIGMA.2011.070
https://nasplib.isofts.kiev.ua/handle/123456789/147393
We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in this theory with the Frobenius-Schur indicator on the representation. We relate any complex simple Klein TFT to a real division ring.
We are grateful to P. Deligne, B. Feigin, Yu. Manin, S. Shadrin and V. Turaev for useful
 discussions. Part of this work was done during the stays of S.N. at Max-Planck-Institute in
 Bonn, he is grateful to MPIM for their hospitality and support. The work of S.N. was partly
 supported by grants RFBR-11-01-00289, N.Sh-8462.2010.1 and the Russian government grant 11.G34.31.0005. The work of S.L. was partly supported by grants: N.Sh-3035.2008.2, RFBR-09-01-00242, SU-HSE award No.09-09-0009, RFBR-CNRS-07-01-92214, RFBR-IND-08-01-91300, RFBR-CNRS-09-01-93106 and P. Deligne 2004 Balzan prize in mathematics.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Klein Topological Field Theories from Group Representations
Article
published earlier
spellingShingle Klein Topological Field Theories from Group Representations
Loktev, S.A.
Natanzon, S.M.
title Klein Topological Field Theories from Group Representations
title_full Klein Topological Field Theories from Group Representations
title_fullStr Klein Topological Field Theories from Group Representations
title_full_unstemmed Klein Topological Field Theories from Group Representations
title_short Klein Topological Field Theories from Group Representations
title_sort klein topological field theories from group representations
url https://nasplib.isofts.kiev.ua/handle/123456789/147393
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