VI.—Complex Four-dimensional Lie Algebras

Abstract

SynopsisCanonical forms of the four-dimensional complex Lie algebras are obtained by considering the roots of certain well-defined vectors of the algebras. A complete set of characters of the algebras is also given, enabling any given four-dimensional complex Lie algebra to be identified with one of the canonical forms.

Lie algebras of genus one and genus two

“…His paper contains errors, which have been documented in Patterson [8] and Marshall [7]. Wallace [9] has obtained a classification of Lie algebras of dimension four over the complex numbers. It should be remarked that not unlike Wallace, who was unaware of Knebelman's work, the author was unaware of both Wallace's and Knebelman's work until quite recently.…”