Twisted quantum toroidal algebras $T_q^-(\mathfrak g)$

TL;DR

This paper constructs a twisted quantum toroidal algebra associated with Kac-Moody algebras, introducing a new algebraic structure with quantum Serre relations, expanding the framework of quantum loop algebras.

Contribution

It introduces a twisted quantum toroidal algebra for Kac-Moody algebras, including quantum Serre relations, which is a novel extension in quantum algebra theory.

Findings

Construction of a principally graded quantum loop algebra.

Derivation of a twisted quantum toroidal algebra.

Establishment of quantum Serre relations for the new algebra.

Abstract

We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.