Classical and Quantum $V$-algebras

Abstract

The problem of the classification of the extensions of the Virasoro algebra is discussed. It is shown that all $H$-reduced ${\hat{\mathcal{G}}}_r$-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.

Latex, 20 pages

References in corpus (1)

• Parafermionic Reductions of WZW Model

Cited by in corpus (2)

• Soliton Spectrum of Integrable Models with Local Symmetries
• Solitons with Isospin