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Register a new userRational vertex operator algebras are finitely generated
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It is proved that any vertex operator algebra for which the image of the Virasoro element in Zhus algebra is algebraic over complex numbers is finitely generated. In particular, any vertex operator algebra with a finite dimensional Zhus algebra is finitely generated. As a result, any rational vertex operator algebra is finitely generated.
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The rational and C_2-cofinite simple vertex operator algebras whose effective central charges and the central charges c are equal and less than 1 are classified. Such a vertex operator algebra is zero if c<0 and C if c=0. If c>0, it is an extension of discrete Virasoro vertex operator algebra L(c_{p,q},0) by its irreducible modules. It is also proved that for any rational and C_2-cofinite simple vertex operator algebra whose effective central charge and central charge are equal, the vertex operator subalgebra generated by the Virasoro vector is simple.
In this paper, I investigate the ascending chain condition of right ideals in the case of vertex operator algebras satisfying a finiteness and/or a simplicity condition. Possible applications to the study of finiteness of orbifold VOAs is discussed.
It is proved that the parafermion vertex operator algebra associated to the irreducible highest weight module for the affine Kac-Moody algebra A_1^{(1)} of level k coincides with a certain W-algebra. In particular, a set of generators for the parafermion vertex operator algebra is determined.
The structure of the parafermion vertex operator algebra associated to an integrable highest weight module for any affine Kac-Moody algebra is studied. In particular, a set of generators for this algebra has been determined.
In the present paper we show that Hall algebras of finitary exact categories behave like quantum groups in the sense that they are generated by indecomposable objects. Moreover, for a large class of such categories, Hall algebras are generated by their primitive elements, with respect to the natural comultiplication, even for non-hereditary categories. Finally, we introduce certain primitively generated subalgebras of Hall algebras and conjecture an analogue of Lie correspondence for those finitary categories.
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