Structure of the Enveloping Algebras

In: Acta polytechnica: journal of advanced engineering, Band 47, Heft 2-3

Abstract

The adjoint representations of several small dimensional Lie algebras on their universal enveloping algebras are explicitly decomposed. It is shown that commutants of raising operators are generated as polynomials in several basic elements. The explicit form of these elements is given and the general method for obtaining these elements is described.