Classical and Quantum $V$-algebras

Details Classical and Quantum $V$-algebras Classical and Quantum $V$-algebras

1998-10-01

arxiv.org/abs/hep-th/9810011v1

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 20 pages

Scientific paper

The problem of the classification of the extensions of the Virasoro algebra is discussed. It is shown that all $H$-reduced $\hat{\cal G}_{r}$-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 $V_{3}^{(1,1)}$-algebra.

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