Systems of quotients of Lie triple systems

TL;DR

This paper introduces the concept of systems of quotients for Lie triple systems, explores their properties, and establishes connections with Martindale-like quotients and algebra of quotients, enabling the construction of maximal systems.

Contribution

It defines systems of quotients for Lie triple systems and links them to existing quotient concepts, providing a framework for maximal quotient construction.

Findings

System of quotients is equivalent to algebra of quotients in some sense.

Maximal system of quotients can be constructed for nondegenerate Lie triple systems.

Connections established between Lie triple systems and Lie algebra quotients.

Abstract

In this paper, we introduce the notion of system of quotients of Lie triple systems and investigate some properties which can be lifted from a Lie triple system to its systems of quotients. We relate the notion of Lie triple system of Martindale-like quotients with respect to a filter of ideals and the notion of system of quotients, and prove that the system of quotients of a Lie triple system is equivalent to the algebra of quotients of a Lie algebra in some sense, and these allow us to construct the maximal system of quotients for nondegenerate Lie triple systems.