Classical and Quantum V-algebras

1998/10/01 by Gomes, J. F., da Silveira, F. E. Mendonça, Sotkov, G. M. +1
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.hep-th/9810011

Abstract

The problem of the classification of the extensions of the Virasoro algebra is discussed. It is shown that all H-reduced \cal G_r-current algebras belong to one of the following basic algebraic structures: local quadratic W-algebras, rational U-algebras, nonlocal V-algebras, nonlocal quadratic WV-algebras and rational nonlocal UV-algebras. The main new features of the quantum V-algebras and their heighest weight representations are demonstrated on the example of the quantum V₃^(1,1)-algebra.

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