Abstract
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 provides such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of 3-junctions of strings and membranes. Generalizations are also considered.
| Original language | English (US) |
|---|---|
| Article number | 505401 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 43 |
| Issue number | 50 |
| DOIs | |
| State | Published - Dec 17 2010 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)
Cite this
Hypermatrix factors for string and membrane junctions. / Fang, Yuhan; Levkowitz, Shir; Sati, Hisham; Thompson, Daniel.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 50, 505401, 17.12.2010.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Hypermatrix factors for string and membrane junctions
AU - Fang, Yuhan
AU - Levkowitz, Shir
AU - Sati, Hisham
AU - Thompson, Daniel
PY - 2010/12/17
Y1 - 2010/12/17
N2 - 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 provides such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of 3-junctions of strings and membranes. Generalizations are also considered.
AB - 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 provides such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of 3-junctions of strings and membranes. Generalizations are also considered.
UR - http://www.scopus.com/inward/record.url?scp=78649759357&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78649759357&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/43/50/505401
DO - 10.1088/1751-8113/43/50/505401
M3 - Article
AN - SCOPUS:78649759357
VL - 43
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 50
M1 - 505401
ER -