Vertex Ring-Indexed Lie Algebras

TL;DR

This paper introduces new infinite-dimensional Lie algebras indexed by cyclotomic rings, generalizing the Onsager algebra and potentially impacting conformal field theory, brane physics, and materials science.

Contribution

It defines a class of partially graded Lie algebras on cyclotomic rings, extending the structure of known algebras like the Onsager algebra.

Findings

Algebras are specified by indices on cyclotomic rings.

They generalize the Onsager algebra and are not subalgebras of loop algebras.

Potential applications in CFT, brane physics, and graphite monolayers.

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 generalizations of the Onsager algebra, but unlike it, or its sl(n) generalizations, they are not subalgebras of the loop algebras associated with sl(n). In a particular interesting case associated with sl(3), their indices lie on the Eisenstein integer triangular lattice, and these algebras are expected to underlie vertex operator combinations in CFT, brane physics, and graphite monolayers.