2013/05/29 by Furutani, Kenro, Markina, Irina
#17B30 #22E25 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1305.6814
Let \mathscr N be a two step nilpotent Lie algebra endowed with non-degenerate scalar product ⟨⋅ ,⋅⟩ and let \mathscr N=V⊕⊥Z, where Z is the center of the Lie algebra and V its orthogonal complement with respect to the scalar product. We prove that if (V,⟨⋅ ,⋅⟩V) is the Clifford module for the Clifford algebra \Cl(Z,⟨⋅ ,⋅⟩Z) such that the homomorphism J\colon \Cl(Z,⟨⋅ ,⋅⟩Z)→\End(V) is skew symmetric with respect to the scalar product ⟨⋅ ,⋅⟩V, or in other words the Lie algebra \mathscr N satisfies conditions of general H-type Lie algebras ~\citeCiatti, GKM, then there is a basis with respect to which the structural constants of the Lie algebra \mathscr N are all ± 1 or 0.