Finite Dimensional Grading of the Virasoro Algebra
Identifieur interne : 000A15 ( Main/Merge ); précédent : 000A14; suivant : 000A16Finite Dimensional Grading of the Virasoro Algebra
Auteurs : Rubén A. Hidalgo [Chili] ; Irina Markina [Norvège] ; Alexander Vasil'Ev [Norvège]Source :
- Georgian Mathematical Journal [ 1072-947X ] ; 2007-09.
English descriptors
- KwdEn :
- Algebra, Algebra vect, Anal, Analytic component, Analytic functions, Analytic representation, Banach space, Beltrami, Beltrami equation, Boundary functions, Central extension, Coadjoint orbits, Commutation rule, Commutator relations, Complex structure, Conformal, Conformal maps, Conformal welding, Eld, Embedding, English transl, Fuchsian, Fuchsian group, Fuchsian groups, Functional form, Graduate texts, Hamiltonian, Hamiltonian function, Hamiltonian system, Hamiltonian systems, Harmonic beltrami, Hidalgo, Holomorphic, Holomorphic functions, Initial point, Integrable, Integrable system, Integrable systems, John wiley sons, Markina, Nite, Nite spaces, Pairwise involutory, Partial integrability, Pures appl, Quasiconformal, Quasiconformal extension, Real case, Recurrence relation, Schlicht functions, Second edition, Smooth contours, Tangent space, Unit circle, Unit disk, Univalent, Univalent function, Univalent functions, Universal space, Vect, Vector space, Virasoro, Virasoro algebra, Virasoro generators, Witt algebra.
- Teeft :
- Algebra, Algebra vect, Anal, Analytic component, Analytic functions, Analytic representation, Banach space, Beltrami, Beltrami equation, Boundary functions, Central extension, Coadjoint orbits, Commutation rule, Commutator relations, Complex structure, Conformal, Conformal maps, Conformal welding, Eld, Embedding, English transl, Fuchsian, Fuchsian group, Fuchsian groups, Functional form, Graduate texts, Hamiltonian, Hamiltonian function, Hamiltonian system, Hamiltonian systems, Harmonic beltrami, Hidalgo, Holomorphic, Holomorphic functions, Initial point, Integrable, Integrable system, Integrable systems, John wiley sons, Markina, Nite, Nite spaces, Pairwise involutory, Partial integrability, Pures appl, Quasiconformal, Quasiconformal extension, Real case, Recurrence relation, Schlicht functions, Second edition, Smooth contours, Tangent space, Unit circle, Unit disk, Univalent, Univalent function, Univalent functions, Universal space, Vect, Vector space, Virasoro, Virasoro algebra, Virasoro generators, Witt algebra.
Abstract
The Virasoro algebra is a central extension of the Witt algebra, the complexified Lie algebra of the sense preserving diffeomorphism group of the circle Diff 𝑆1. It appears in Quantum Field Theories as an infinite dimensional algebra generated by the coefficients of the Laurent expansion of the analytic component of the momentum-energy tensor, Virasoro generators. The background for the construction of the theory of unitary representations of Diff 𝑆1 is found in the study of Kirillov's manifold Diff 𝑆1=𝑆1. It possesses a natural Kählerian embedding into the universal Teichmüller space with the projection into the moduli space realized as an infinite-dimensional body of the coefficients of univalent quasiconformally extendable functions. The differential of this embedding leads to an analytic representation of the Virasoro algebra based on Kirillov's operators. In this paper we overview several interesting connections between the Virasoro algebra, Teichmüller theory, Löwner representation of univalent functions, and propose a finite-dimensional grading of the Virasoro algebra such that the grades form a hierarchy of finite dimensional algebras which, in their turn, are the first integrals of Liouville partially integrable systems for coefficients of univalent functions.
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DOI: 10.1515/GMJ.2007.419
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It appears in Quantum Field Theories as an infinite dimensional algebra generated by the coefficients of the Laurent expansion of the analytic component of the momentum-energy tensor, Virasoro generators. The background for the construction of the theory of unitary representations of Diff 𝑆1 is found in the study of Kirillov's manifold Diff 𝑆1=𝑆1. It possesses a natural Kählerian embedding into the universal Teichmüller space with the projection into the moduli space realized as an infinite-dimensional body of the coefficients of univalent quasiconformally extendable functions. The differential of this embedding leads to an analytic representation of the Virasoro algebra based on Kirillov's operators. In this paper we overview several interesting connections between the Virasoro algebra, Teichmüller theory, Löwner representation of univalent functions, and propose a finite-dimensional grading of the Virasoro algebra such that the grades form a hierarchy of finite dimensional algebras which, in their turn, are the first integrals of Liouville partially integrable systems for coefficients of univalent functions.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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