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 |
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| Дата: | 2011 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2011
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| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862721134549532672 |
|---|---|
| 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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| first_indexed | 2025-12-07T18:29:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147393 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:29:17Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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 |
| work_keys_str_mv | AT loktevsa kleintopologicalfieldtheoriesfromgrouprepresentations AT natanzonsm kleintopologicalfieldtheoriesfromgrouprepresentations |