It is known that the centerless Zamolodchikov--$w_{\infty}$ $*$--Lie algebra of conformal field theory does not admit nontrivial central extensions, but the Witt $*$--Lie algebra, which is a sub--algebra of $w_{\infty}$, admits a nontrivial central extension: the Virasoro algebra. Therefore the following question naturally arises: {\it are there other natural sub--algebras of $w_{\infty}$ which admit nontrivial central extensions other than the Virasoro one?} We show that for certain infinite dimensional closed subalgebras of $w_{\infty}$, which are natural generalizations of the Witt algebra the answer is negative.
Accardi, L., Boukas, A. (2013). Central extension of Virasoro type subalgebras of the Zamolodchikov--$w_{\infty}$ Lie algebra. In L. Accardi, F. Fagnola (a cura di), Quantum probability and related topics: proceedings of the 32nd conference, Levico Terme, Italy, 29 May – 4 June 2011 (pp. 1-16). World Scientific Publishing Co. [10.1142/9789814447546_0001].
Central extension of Virasoro type subalgebras of the Zamolodchikov--$w_{\infty}$ Lie algebra
ACCARDI, LUIGI;
2013-01-01
Abstract
It is known that the centerless Zamolodchikov--$w_{\infty}$ $*$--Lie algebra of conformal field theory does not admit nontrivial central extensions, but the Witt $*$--Lie algebra, which is a sub--algebra of $w_{\infty}$, admits a nontrivial central extension: the Virasoro algebra. Therefore the following question naturally arises: {\it are there other natural sub--algebras of $w_{\infty}$ which admit nontrivial central extensions other than the Virasoro one?} We show that for certain infinite dimensional closed subalgebras of $w_{\infty}$, which are natural generalizations of the Witt algebra the answer is negative.File | Dimensione | Formato | |
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