Structure of the Enveloping Algebras

Č. Burdík, O. Navrátil, S. Pošta

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. 

Keywords


adjoint representation; enveloping algebra; Lie algebra

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague