Abstract
This chapter discusses a set of maximal subfields in the quotient division ring of an enveloping algebra and considers a finite dimensional Lie algebra over a specific field of characteristic zero. The enveloping algebra of the maximal subfields is provided with a quotient division ring. The chapter illustrates an analogous result for the quotient division ring of a group ring in which a commutative intergral domain and a torsion-free nilpotent group are considered. It also discusses commutative polarization with respect to a regular linear function. The phenomenon of commutative polarization occurs frequently in the nilpotent case, but never in the semi-simple case.
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