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The Kac-moody and Virasoro commutation equations
Institution:1. Department of Physics, University of Colorado, Boulder, CO 80309, USA;2. Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA;1. Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 180 Siwangting Road, Yangzhou City, Jiangsu Province 225002, China;2. Shanghai Frontier Science Center for Gravitational Wave Detection, School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China
Abstract:The commutation equation of the Kac-Moody generators realized as functional differential operators is explicitly verified. The anomaly of the loop group generators is briefly discussed and the Virasoro commutation equation is then derived. No use is made of normal ordering in obtaining the central extensions of the above commutation equations.
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