T*-extension of a 3-Lie algebra

Abstract

We introduce a new technique called T*-extension, of constructing a metric 3-Lie algebra out of an arbitrary 3-Lie algebra, and explore all possible metrics and corresponding signatures on this resulting metric 3-Lie algebra.

Keywords:

• 3-Lie algebra
• metric
• representation of a 3-Lie algebra
• T*-extension

AMS Subject Classifications::

• 17B20
• 17B81