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2002•Reviews in Mathematical PhysicsRequires access

FORMAL AND ANALYTIC DEFORMATIONS FROM WITT TO VIRASORO

Luca Guerrini

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Abstract

We introduce a new family [Formula: see text] of deformations of the Witt algebra [Formula: see text], F varying in the space of all polynomials with vanishing constant terms, and show the existence of an isomorphism of its formal and analytic completions with those of the Witt algebra. Central extensions of this algebra are considered and the existence of an isomorphism between their formal and analytic completions with those of the Virasoro algebra is proved.

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We introduce a new family [Formula: see text] of deformations of the Witt algebra [Formula: see text], F varying in the space of all polynomials with vanishing constant terms, and show the existence of an isomorphism of its formal and analytic completions with those of the Witt algebra. Central extensions of this algebra are considered and the existence of an isomorphism between their formal and analytic completions with those of the Virasoro algebra is proved.

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Available abstract

We introduce a new family [Formula: see text] of deformations of the Witt algebra [Formula: see text], F varying in the space of all polynomials with vanishing constant terms, and show the existence of an isomorphism of its formal and analytic completions with those of the Witt algebra. Central extensions of this algebra are considered and the existence of an isomorphism between their formal and analytic completions with those of the Virasoro algebra is proved.

Key concepts: Witt algebra, Virasoro algebra, Isomorphism (crystallography), Mathematics, Algebra over a field, Pure mathematics, Constant (computer programming), Cellular algebra

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