Quantum group GL_<var>q</var>(2) and quantum Laplace operator via semi-infinite cohomology

Abstract

We construct the quantum group $\mathrm{GL}_q(2)$ 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.