We argue that a description of supersymmetric extended objects from a unified
geometric point of view requires an enlargement of superspace. To this aim we
study in a systematic way how superspace groups and algebras arise from
Grassmann spinors when these are assumed to be the only primary entities. In
the process, we recover generalized spacetime superalgebras and extensions of
supersymmetry found earlier. The enlargement of ordinary superspace with new
parameters gives rise to extended superspace groups, on which manifestly
supersymmetric actions may be constructed for various types of p-branes,
including D-branes (given by Chevalley-Eilenberg cocycles) with their
Born-Infeld fields. This results in a field/extended superspace democracy for
superbranes: all brane fields appear as pull-backs from a suitable target
superspace. Our approach also clarifies some facts concerning the origin of the
central charges for the different p-branes.Comment: Latex file, 31 pgs. Version to appear in NP
The forms of the invariant primitive tensors for the simple Lie algebras A_l,
B_l, C_l and D_l are investigated. A new family of symmetric invariant tensors
is introduced using the non-trivial cocycles for the Lie algebra cohomology.
For the A_l algebra it is explicitly shown that the generic forms of these
tensors become zero except for the l primitive ones and that they give rise to
the l primitive Casimir operators. Some recurrence and duality relations are
given for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3)
and su(4) are also provided. Finally, new relations involving the d and f su(n)
tensors are given.Comment: Latex file. 34 pages. (Trivial) misprints corrected. To appear in
Nucl. Phys.
It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their generalised Jacobi identities turn out to be satisfied by the antisymmetric tensors (or higher-order 'structure constants') which characterise the Lie algebra cocycles. This analysis allows us to present a classification of the higherorder simple Lie algebras as well as a constructive procedure for them. Our results are synthesised by the introduction of a single, complete BRST operator associated with each simple algebra.
The OSp(2͉2)-invariant planar dynamics of a Dϭ4 superparticle near the horizon of a large mass extreme black hole is described by an Nϭ2 superconformal mechanics, with the SO(2) charge being the superparticle's angular momentum. The non-manifest superconformal invariance of the superpotential term is shown to lead to a shift in the SO(2) charge by the value of its coefficient, which we identify as the orbital angular momentum. The full SU(1,1͉2) invariant dynamics is found from an extension to Nϭ4 superconformal mechanics. ͓S0556-2821͑99͒01608-2͔
Newly introduced generalized Poisson structures based on suitable skew-symmetric contravariant tensors of even order are discussed in terms of the Schouten-Nijenhuis bracket. The associated 'Jacobi identities' are expressed as conditions on these tensors, the cohomological contents of which is given. In particular, we determine the linear generalized Poisson structures which can be constructed on the dual spaces of simple Lie algebras. †
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