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

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