Abelian hypercomplex structures on central extensions of H-type Lie algebras

✍ Scribed by Marı́a Laura Barberis

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 102 KB
• Volume: 158
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(00)00022-0

✦ Synopsis

It is the aim of this work to give a characterization of the two-step nilpotent Lie algebras carrying abelian hypercomplex structures. In the special case of trivial extensions of irreducible H -type Lie algebras this characterization is given in terms of the dimension of the commutator subalgebra. As a consequence, we obtain the corresponding theorem for arbitrary H -type Lie algebras, extending a result in Barberis and Dotti, J. Math. Oxford (2) 47 (1996) 389 -404.