Matryoshka of special democratic forms
- Special p-forms are forms which have components fµ1…µp equal to +1, -1 or 0 in some orthonormal basis. A p-form ϕ ∈ � pRd is called democratic if the set of nonzero components {ϕμ1...μp} is symmetric under the transitive action of a subgroup of O(d,Z) on the indices {1, . . . , d}. Knowledge of these symmetry groups allows us to define mappings of special democratic p-forms in d dimensions to special democratic P-forms in D dimensions for successively higher P = p and D = d. In particular, we display a remarkable nested structure of special forms including a U(3)-invariant 2-form in six dimensions, a G2-invariant 3-form in seven dimensions, a Spin(7)-invariant 4-form in eight dimensions and a special democratic 6-form O in ten dimensions. The latter has the remarkable property that its contraction with one of five distinct bivectors, yields, in the orthogonal eight dimensions, the Spin(7)-invariant 4-form. We discuss various properties of this ten dimensional form.
Author details: | Chandrashekar DevchandORCiD, Jean Nuyts, Gregor Weingart |
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URN: | urn:nbn:de:kobv:517-opus4-429002 |
DOI: | https://doi.org/10.25932/publishup-42900 |
ISSN: | 1866-8372 |
Title of parent work (German): | Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (841) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2020/03/10 |
Publication year: | 2009 |
Publishing institution: | Universität Potsdam |
Release date: | 2020/03/10 |
Tag: | commutator subgroup; cycle decomposition; democratic form; special holonomy; transitive action |
Issue: | 841 |
Number of pages: | 20 |
First page: | 545 |
Last Page: | 562 |
Source: | Communications in Mathematical Physics 293 (2010) 545 545–562 DOI: 10.1007/s00220-009-0939-5 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
Peer review: | Referiert |
Publishing method: | Open Access |
License (German): | Creative Commons - Namensnennung-Nicht kommerziell 2.0 Generic |
External remark: | Bibliographieeintrag der Originalveröffentlichung/Quelle |