"Cayley-Klein" schemes for real Lie algebras and Freudhental Magic Squares
Santander, Mariano ; Herranz, Francisco J.
arXiv, 9702031 / Harvested from arXiv
Text on arXiv
We introduce three "Cayley-Klein" families of Lie algebras through realizations in terms of either real, complex or quaternionic matrices. Each family includes simple as well as some limiting quasi-simple real Lie algebras. Their relationships naturally lead to an infinite family of $3\times 3$ Freudenthal-like magic squares, which relate algebras in the three CK families. In the lowest dimensional cases suitable extensions involving octonions are possible, and for $N=1, 2$, the "classical" $3\times 3$ Freudenthal-like squares admit a $4\times 4$ extension, which gives the original Freudenthal square and the Sudbery square.
Publié le : 1997-02-24
Classification:  Mathematical Physics 
@article{9702031,
     author = {Santander, Mariano and Herranz, Francisco J.},
     title = {"Cayley-Klein" schemes for real Lie algebras and Freudhental Magic
  Squares},
     journal = {arXiv},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9702031}
}

Santander, Mariano; Herranz, Francisco J. "Cayley-Klein" schemes for real Lie algebras and Freudhental Magic
  Squares. arXiv, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/9702031/