Application of Cartan groups in physics

Author: Alexandre Gurchumelia
Keywords: Lie groups, Exceptional group G2, Casimir operator
Annotation:

This work overviews classification of Lie groups and their several properties (roots, Dynkin diagrams, Casimir operators and etc.). Exceptional non-compact Cartan group G₂ and its geometric application is considered. The second order Casimir operator for this group has been found and it is shown that in a special case the operator can be represented as the sum of two independent Casimir operators of Poincaré group.