Hypermatrix factors for string and membrane junctions

Details Hypermatrix factors for string and membrane junctions Hypermatrix factors for string and membrane junctions

2010-01-28

arxiv.org/abs/1001.5166v2

J.Phys.A43:505401,2010

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 4 figures, presentation improved, minor corrections

Scientific paper

10.1088/1751-8113/43/50/505401

The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric products of two vector spaces, and hence are matrix representations. We consider the analogous products of three vector spaces and study when they appear as summands in Lie algebra decompositions. The Z3-grading of the exceptional Lie algebras provide such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of three-junctions of strings and membranes. Generalizations are also considered.

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