Immediate applications of a new classification of finite dimensional simple Lie algebras

We present three important applications of a new classification of simple Lie algebras. The first one consists in the determination of a scalar series (C_q ) _q≥0 related to Casimir elements, associated with a simple Lie algebra. The second one consists in the determination of the spectral decomposition of the square tensor of a simple Lie algebra. Finally the third application consists in a simple characterization of Lie superalgebras of type Q ( n ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187674/f8337d7b-6b74-4da5-ae84-c225ed353b0a/content/pg55_1.tif"/> . We present also a brief presentation of the new classification mentioned above.