Quantum Group $GL_q(2)$ and Quantum Laplace Operator via Semi-infinite Cohomology

TL;DR

This paper constructs the quantum group $GL_q(2)$ using semi-infinite cohomology of braided vertex operator algebras and introduces a conformal field theory version of the Laplace operator on this quantum group.

Contribution

It presents a novel construction of $GL_q(2)$ via semi-infinite cohomology and derives a conformal field theory analogue of the Laplace operator.

Findings

Quantum group $GL_q(2)$ constructed from vertex operator algebras.

Conformal field theory version of the Laplace operator obtained.

Provides a new algebraic and analytical framework for quantum groups.

Abstract

We construct the quantum group $GL_q(2)$ as the semi-infinite cohomology of the tensor product of two braided vertex operator algebras based on the algebra $W_2$ with complementary central charges $c+\bar{c}=28$. The conformal field theory version of the Laplace operator on the quantum group is also obtained.