@article{DevchandNuytsWeingart2010,
  author    = {Devchand, Chandrashekar and Nuyts, Jean and Weingart, Gregor},
  title     = {Matryoshka of Special Democratic Forms},
  issn      = {143-0916},
  year      = {2010},
  abstract  = {Special p-forms are forms which have components phi_{mu_1...mu_p} equal to +1,-1 or 0 in some orthonormal basis. A p-form phiin Lambda^p R^d is called democratic if the set of nonzero components {phi_{mu_1...mu_p}} 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 geq p and D geq d. In particular, we display a remarkable nested stucture of special forms including a U(3)-invariant 2-form in six dimensions, a G_2-invariant 3-form in seven dimensions, a Spin(7)- invariant 4-form in eight dimensions and a special democratic 6-form Omega 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.},
  language  = {en}
}
@article{DevchandFairlieNuytsetal.2009,
  author    = {Devchand, Chandrashekar and Fairlie, David and Nuyts, Jean and Weingart, Gregor},
  title     = {Ternutator identities},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8113/42/47/475209},
  year      = {2009},
  abstract  = {The ternary commutator or ternutator, defined as the alternating sum of the product of three operators, has recently drawn much attention as an interesting structure generalizing the commutator. The ternutator satisfies cubic identities analogous to the quadratic Jacobi identity for the commutator. We present various forms of these identities and discuss the possibility of using them to define ternary algebras.},
  language  = {en}
}