Vertex ring-indexed lie algebras.

Abstract

Infinite dimensional Lie algebras are introduced, which are only partially graded, and are specified by indices lying on cyclotomic rings. They may be thought of as generalisations of the Onsager algebra, but unlike it or its sl(n) generalisations, they are not subalgebras of loop algebras associated with sln(n). In a particularly interesting ase associalte with sl(3), their indices lie on the Eisenstein integer triangular lattice and these algebras are expected to undelie vertex operator combinations in CFT, brane physics and graphite monolayers.