Poisson Bracket Realizations of Lie Algebras and Subrepresentations of (Adsup(Xk))sub(S)

摘要

A procedure which associates Poisson bracket realizations of a Lie Algebra L to subrepresentations of the extension (adsup(xk))Sub(s) of the adjoint action to the algebra of polynomials defined on the dual space Lsup(*) is pointed out. The procedure is applied, for k = 2, to the real forms of the semisimple Lie algebras of types D sub 3 and B sub 2 approximately C sub 2 , in particular to the algebras so (4,2), so (4,1) and so (3,2) approximately sp (4,R). The results obtained for the algebra sp (4,R) have lead to an algebraic foundation for the constraints satisfied by the dynamical variables for the classical limit of the generalized Helium problem. (Atomindex citation 15:042332)