CLASSIFICATION OF SIX-DIMENSIONAL REAL DRINFELD DOUBLES

Abstract

Starting from the classification of real Manin triples we look for those that are isomorphic as six-dimensional Drinfeld doubles i.e. Lie algebras with the ad-invariant form used for construction of the Manin triples. We use several invariants of the Lie algebras to distinguish the nonisomorphic structures and give the explicit form of maps between Manin triples that are decompositions of isomorphic Drinfeld doubles. The result is a complete list of six-dimensional real Drinfeld doubles. It consists of 22 classes of nonisomorphic Drinfeld doubles.