Structure theory of finite conformal algebras
type: Item
instance of: scholarly article
title: Structure theory of finite conformal algebras
zbMATH Open document ID: 0918.17019
author: Alessandro D'Andrea
author: Victor G. Kac
published in: Selecta Mathematica. New Series
publication date: 1999-08-17T00:00:00Z
full work available at URL: http://hdl.handle.net/1721.1/47476
review text: 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.
reviewed by: Dražen Adamović
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 17B69
zbMATH DE Number: 1236206
zbMATH Keywords: conformal algebra
zbMATH Keywords: finite conformal algebra
zbMATH Keywords: conformal module
zbMATH Keywords: formal distribution Lie algebra
MaRDI profile type: Publication
OpenAlex ID: W1988051979
DOI: 10.1007/S000290050036
description: scientific article; zbMATH DE number 1236206