Groeger, Josua (2016). The twofold way of super holonomy. Forum Math., 28 (6). S. 1031 - 1051. BERLIN: WALTER DE GRUYTER GMBH. ISSN 1435-5337
Full text not available from this repository.Abstract
There are two different notions of holonomy in supergeometry, the supergroup introduced by Galaev and our functorial approach motivated by super Wilson loops. Either theory comes with its own version of invariance of vectors and subspaces under holonomy. By our first main result, the Twofold Theorem, these definitions are equivalent. Our proof is based on the Comparison Theorem, our second main result, which characterises Galaev's holonomy algebra as an algebra of coefficients, building on previous results. As an application, we generalise some of Galaev's results to S-points, utilising the holonomy functor. We obtain, in particular, a de Rham-Wu decomposition theorem for semi-Riemannian S-supermanifolds.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-257090 | ||||||||
| DOI: | 10.1515/forum-2015-0139 | ||||||||
| Journal or Publication Title: | Forum Math. | ||||||||
| Volume: | 28 | ||||||||
| Number: | 6 | ||||||||
| Page Range: | S. 1031 - 1051 | ||||||||
| Date: | 2016 | ||||||||
| Publisher: | WALTER DE GRUYTER GMBH | ||||||||
| Place of Publication: | BERLIN | ||||||||
| ISSN: | 1435-5337 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| Refereed: | Yes | ||||||||
| URI: | http://kups.ub.uni-koeln.de/id/eprint/25709 |
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