Graded systems of quotients and Martindale-like quotients of graded Lie triple systems

Abstract

The paper is devoted to introducing graded systems of quotients of graded Lie triple systems, graded weak systems of quotients of graded Lie triple systems and graded systems of Martindale-like quotients of graded Lie triple systems with respect to power graded filters of sturdy graded ideals. And then we investigate certain vital properties of graded Lie triple systems, which can be lifted from a graded Lie triple system to its graded systems of quotients. Furthermore, the connections among graded systems of quotients, graded weak systems of quotients and graded systems of Martindale-like quotients are surveyed. What’s more, the relationship between graded systems of quotients of graded Lie triple systems and systems of quotients of Lie triple systems is highlighted. Besides, the relationship between graded systems of quotients of a graded Lie triple system and graded algebras of quotients of the graded Lie algebra L(T) (the standard embedding of a graded Lie triple system T) is considered, too.

KEYWORDS:

• Graded Lie triple systems
• graded systems of quotients
• Martindale-like quotients

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B70
• 17B99

Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Additional information

Funding

Supported by NSF of Jilin Province (No. YDZJ202201ZYTS589), NNSF of China (Nos. 12271085, 12071405, 11801066), CSC of China (202106625001) and the Fundamental Research Funds for the Central Universities.