Representations of Quantum Minimal Surface Algebrasvia Kac-Moody-theory

TL;DR

This paper explores the structure of quantum minimal surface algebras by constructing epimorphisms onto involutory subalgebras of split real simply-laced Kac-Moody algebras, including affine and finite types, with extensions to complex cases.

Contribution

It introduces new epimorphisms from quantum minimal surface algebras onto Kac-Moody subalgebras and the algebras themselves, expanding understanding of their representations.

Findings

Examples of epimorphisms onto affine and finite type Kac-Moody algebras

Construction of epimorphisms onto Kac-Moody algebras with real structures

Extension of results to complex Kac-Moody algebras

Abstract

We consider epimorphisms from quantum minimal surface algebras onto involutroy subalgebras of split real simply-laced Kac-Moody algebras and provide examples of affine and finite type. We also provide epimorphisms onto such Kac-Moody algebras themselves, where reality of the construction is important. The results extend to the complex situation.