T *-extension of n-Lie algebras

Abstract

We introduce a new technique, called the T *-extension, of constructing metric n-Lie algebras from arbitrary ones and obtain some important properties on this extension. Finally, we investigate the metric n-Lie algebras that are isometric to certain T *-extensions.

Keywords:

• T *-extension
• metric n-Lie algebra
• invariant scalar product

AMS Subject Classifications::

• 17A42
• 17A45
• 17B50

Acknowledgements

The authors are very grateful to the referees for their patient reading and valuable comments, which improved the appearance and readability of this article.