A quantized Tits-Kantor-Koecher algebra

TL;DR

This paper introduces a quantum version of the Tits-Kantor-Koecher algebra using vertex operator constructions over a Fock space, expanding the algebraic framework into the quantum domain.

Contribution

It presents the first quantum analogue of the Tits-Kantor-Koecher algebra with a Jordan torus as the coordinate algebra, constructed via vertex operators.

Findings

Defined a quantum Tits-Kantor-Koecher algebra

Established vertex operator construction over Fock space

Extended classical algebra to quantum setting

Abstract

We propose a quantum analogue of a Tits-Kantor-Koecher algebra with a Jordan torus as an coordinated algebra by looking at the vertex operator construction over a Fock space.