Abstract
3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. In this paper, we provide a construction of 3-Lie algebras in terms of Lie algebras and certain linear functions. Moreover, with the construction from γ-matrices and two-dimensional extensions of metric Lie algebras, all the complex 3-Lie algebras in dimension ≤5 are obtained along this approach. As a special case, we study the structure of the 3-Lie algebras constructed from the general linear Lie algebras with trace forms and prove that they are semisimple and local.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
