Uniformly Distributed Systems of Elements on Metabelian Lie Rings

Abstract

In this article, the notion of a uniformly distributed systems of elements on the variety of metabelian Lie algebras is introduced. This notion is analogous to one of a measure preserving systems of elements on group varieties. As the main result of the article, it was shown that on the variety of metabelian Lie algebras a system of elements is primitive iff it is uniformly distributed.

Key Words:

• Distribution of elements
• Distribution of systems of elements
• Lie rings
• Metabelian

2010 Mathematics Subject Classification:

• 17B01
• 17B30