Structure theory of finite conformal algebras
The theory of conformal algebras initiated in [\textit{V. G. Kac}, Vertex algebras for beginners, Univ. Lect. Ser. 10, AMS (1996; Zbl 0861.17017)], is very useful for the problem of classification of infinite-dimensional Lie algebras. In the present paper the authors investigate a structure theory of finite rank conformal algebras. They show that a finite simple conformal algebra is isomorphic either to current conformal algebra associated with a finite-dimensional simple Lie algebra, or to the Virasoro conformal algebra. A similar result for finite semisimple conformal algebras is also obtained. The authors apply these results to formal distribution Lie algebras. They also study the representation theory of finite conformal algebras and obtain some results which are analogous with the classical results in the theory of finite-dimensional Lie algebras. In particular, they prove the conformal analogues of the Lie theorem and of the Cartan-Jacobson theorem.
scientific article; zbMATH DE number 1236206