Construction of Lie Superalgebras from Triple Product Systems
Susumu Okubo
TL;DR
This paper presents a method to construct simple Lie superalgebras over the complex numbers using triple systems, specifically employing a balanced Freudenthal-Kantor triple system to generate examples like D(2,1;α), G(3), and F(4).
Contribution
It introduces a general construction framework for simple Lie superalgebras from triple systems, expanding the understanding of their algebraic structure.
Findings
Constructed examples of Lie superalgebras D(2,1;α), G(3), F(4)
Utilized a (-1,-1) balanced Freudenthal-Kantor triple system
Provided a unified construction method for simple Lie superalgebras
Abstract
Any simple Lie superalgebras over the complex field can be constructed from some triple systems. Examples of Lie superalgebras , G(3) and F(4) are given by utilizing a general construction method based upon balanced Freudenthal-Kantor triple system.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.