Quantum group $\mathrm{GL}_q(2)$ and quantum Laplace operator via semi-infinite cohomology

Igor B. Frenkel; Anton M. Zeitlin

doi:10.4171/jncg/142

JournalsjncgVol. 7, No. 4pp. 1007–1026

Quantum group $GL_{q} (2)$ and quantum Laplace operator via semi-infinite cohomology

Igor B. Frenkel
Yale University, New Haven, USA
Anton M. Zeitlin
Yale University, New Haven, USA

$Quantum group $\mathrm{GL}_q(2)$ and quantum Laplace operator via semi-infinite cohomology cover$

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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 $c + \overset{c}{ˉ} = 28$ . The conformal field theory version of the Laplace operator on the quantum group is also obtained.

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Igor B. Frenkel, Anton M. Zeitlin, Quantum group $GL_{q} (2)$ and quantum Laplace operator via semi-infinite cohomology. J. Noncommut. Geom. 7 (2013), no. 4, pp. 1007–1026

DOI 10.4171/JNCG/142