Classification of real structures of Lie algebras of fifth order. (Russian) Zbl 0166.04201

Mubarakzyanov, G. M.

Izv. Vyssh. Uchebn. Zaved., Mat. 1963, No. 3(34), 99-106 (1963).

The author gives the classification of five-dimensional real Lie algebras. It is shown that there exists a unique real nonsolvable five-dimensional Lie algebra of the structure \(g_5\): \[ e_1\circ e_2=2e_4,\;e_4\circ e_3=-e_2,\;e_2\circ e_3=2e_3,\;e_1\circ e_4=e_5,\;e_2\circ e_4=e_4,\;e_2\circ e_5=-e_5,\;e_3\circ e_5=e_4. \]

Reviewer: V. Latyshev (R. Zh. Mat. 1963, 11A224)

MSC:

17B30

Solvable, nilpotent (super)algebras

Keywords:

real structures of Lie algebras of fifth order