Laflamme, "The instability of charged black strings and p-branes," Nuclear Physics.

Laflamme, "Black strings and p-branes are unstable," Physical Review Letters, vol.

Horowitz, "Nucleation of p-branes and fundamental strings," Physical Review D: Particles, Fields, Gravitation and Cosmology, vol.

Melnikov, "Toda p-brane black holes and polynomials related to Lie algebras," Classical and Quantum Gravity, vol.

We also mention: the algebraic multispaces (multigroups, multi-rings, multi-vector spaces, multi-operation systems and multi-manifolds, also multi-voltage graphs, multiembedding of a graph in an n-manifold, etc.) or structures included in other structures, geometric multispaces (combinations of Euclidean and Non-Euclidean geometries into one space as in S-geometries), theoretical physics, including the Relativity Theory [4], the M-theory and the cosmology, then multi-space models for

p-branes and cosmology, etc.

(For example, point particles are zero-branes, strings are one-branes, membranes are two-branes, and so on.) For the p-dimensional case, some wag dubbed them p-branes (pronounced "pea brains").

Just as the tail, ear, and leg are different parts of the same lion, the string and various p-branes appear to be different limits of the same theory: M-theory.

According to this idea, the elementary particles arise as vibrations of ten- or eleven-dimensional space-time membranes (called "

p-branes").

Strominger, "Black strings and

p-branes," Nuclear Physics B, vol.

The role of star products in the construction of p-branes actions from the large N limit of SU(N) Yang-Mills can be found in [6] and in the Self-Dual Gravity/SU([infinity]) Self Dual Yang-Mills relation in [7, 8, 9, 10].

In particular, Noncommutative p-brane actions, for even p + 1 = 2n-dimensional world-volumes, were written explicitly [15] in terms of the novel Moyal-Yang (Fedosov-Kontsevich) star product deformations [11, 12] of the Noncommutative Nambu Poisson Brackets (NCNPB) that are associated with the noncommuting world-volume coordinates [q.sup.A], [p.sup.A] for A = = 1, 2, 3, ...

In [8] this Extended Scale Relativity principle was applied to the quantum mechanics of

p-branes which led to the construction of Clifford-space (C-space) where all

p-branes were taken to be on the same footing, in the sense that the transformations in C-space reshuffled a string history for a five-brane history, a membrane history for a string history, for example.