Structure and Representations for the Electrical Lie Algebra of Type D-4

摘要

We prove the dimension conjecture for electrical Lie algebra e(D4) of type D-4. Mo(r)eover, we present a new method to construct 3-step nilpotent Lie algebras and show that e(D4) is isomorphic to the semidirect product of sl(2) with a 3-step nilpotent Lie algebra constructed from the colored complete bipartible graph K-2,K-2. Also, we classify all simple highest weight modules for e(D4).