TY  - GEN
A1  - Devchand, Chandrashekar
A1  - Nuyts, Jean
A1  - Weingart, Gregor
T1  - Matryoshka of special democratic forms
T2  - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 841 
KW  - commutator subgroup
KW  - transitive action
KW  - cycle decomposition
KW  - democratic form
KW  - special holonomy
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-429002
SN  - 1866-8372
IS  - 841
SP  - 545
EP  - 562
ER  -