Geodesic
Extended Affine Root Systems
Journal of Lie theory, Tome 12 (2002) no. 2, pp. 515-527.

Voir la notice de l'article provenant de la source Heldermann Verlag

There are two notions of the extended affine root systems in the literature which both are introduced axiomatically. One, extended affine root system (SAERS for short), consists only of nonisotropic roots, while the other, extended affine root system (EARS for short), contains certain isotropic roots too. We show that there is a one to one correspondence between (reduced) SEARSs and EARSs. Namely the set of nonisotropic roots of any EARS is a (reduced) SEARS, and conversely, there is a unique way of adding certain isotropic elements to a SEARS to get an EARS. (It is known that some of extended affine root systems are not the root system of any extended affine Lie algebra.) 
@article{JLT_2002_12_2_JLT_2002_12_2_a12,
     author = {S. Azam },
     title = {Extended {Affine} {Root} {Systems}},
     journal = {Journal of Lie theory},
     pages = {515--527},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2002},
     url = {http://geodesic.mathdoc.fr/item/JLT_2002_12_2_JLT_2002_12_2_a12/}
}
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S. Azam . Extended Affine Root Systems. Journal of Lie theory, Tome 12 (2002) no. 2, pp. 515-527. http://geodesic.mathdoc.fr/item/JLT_2002_12_2_JLT_2002_12_2_a12/