Geodesic
Lie Algebras Attached to Clifford Modules and Simple Graded Lie Algebras
Journal of Lie theory, Tome 28 (2018) no. 3, pp. 843-864
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We study possible cases of complex simple graded Lie algebras of depth 2, which are the Tanaka prolongations of pseudo H-type Lie algebras arising through representation of Clifford algebras. We show that the complex simple Lie algebras of type Bn with |2|-grading do not contain non-Heisenberg pseudo H-type Lie algebras as their negative nilpotent part, while the complex simple Lie algebras of types An, Cn and Dn provide such a possibility. Among exceptional algebras only F4 and E6 contain non-Heisenberg pseudo H-type Lie algebras as their negative part of |2|-grading. An analogous question addressed to real simple graded Lie algebras is more delicate, and we give results revealing the main differences with the complex situation.
Classification : 17B10, 17B22, 17B25, 22E46
Mots-clés : Simple Lie algebras, root system, Dynkin diagram, graded Lie algebras, parabolic subalgebras, H-type algebra, Clifford algebra, non-degenerate bilinear form 
@article{JLT_2018_28_3_JLT_2018_28_3_a13,
     author = {K. Furutani and M. Godoy Molina and I. Markina and T. Morimoto and A. Vasil'ev},
     title = {Lie {Algebras} {Attached} to {Clifford} {Modules} and {Simple} {Graded} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {843--864},
     year = {2018},
     volume = {28},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2018_28_3_JLT_2018_28_3_a13/}
}
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K. Furutani; M. Godoy Molina; I. Markina; T. Morimoto; A. Vasil'ev. Lie Algebras Attached to Clifford Modules and Simple Graded Lie Algebras. Journal of Lie theory, Tome 28 (2018) no. 3, pp. 843-864. http://geodesic.mathdoc.fr/item/JLT_2018_28_3_JLT_2018_28_3_a13/