Graded Lie Algebras of Dimension Five and Some Artin–Schelter Regular Algebras.

In this paper, we show that there are only seven graded Lie algebras of dimension 5 generated in degree 1 up to isomorphism. By parameterizing the relations of the universal enveloping algebras of three of those graded Lie algebras, we construct some new Artin–Schelter regular algebras of global dimension 5. We prove that those algebras are all strongly noetherian, Auslander regular and Cohen–Macaulay, and describe their Nakayama automorphisms. [ABSTRACT FROM AUTHOR]