Superconformal algebras and transitive group actions on quadrics
type: Item
instance of: scholarly article
title: Superconformal algebras and transitive group actions on quadrics
zbMATH Open document ID: 0886.17021
DOI: 10.1007/BF02885680
author: Victor G. Kac
published in: Communications in Mathematical Physics
publication date: 1998-05-04T00:00:00Z
review text: The author gives a classification of so-called ``physical'' superconformal algebras. The list consists of seven algebras: the Virasoro algebra, the Neveu-Schwarz algebra, the \(N=2,3\) and 4 algebras, the superalgebra of all vector fields on the \(N=2\) supercircle, and a new superconformal algebra constructed by \textit{S.-T. Cheng} and \textit{V. G. Kac} [A new \(N=6\) superconformal algebra, Commun. Math. Phys. 186, No. 1, 219-231 (1997)]. The proof relies heavily on the classification of all the connected subgroups of \(SO_N(\mathbb{C})\) that act transitively on the quadric \((v,v)=1\).
reviewed by: Andrew N. Pressley
Mathematics Subject Classification ID: 17B69
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 1036724
zbMATH Keywords: Lie superalgebra
zbMATH Keywords: formal distribution
zbMATH Keywords: superconformal algebras
MaRDI profile type: Publication
cites work: Les bouts des espaces homogènes de groupes de Lie
cites work: Polar representations
cites work: Lie superalgebras
cites work: Q5687564
cites work: Q4940832
cites work: Classification des algèbres de Lie graduées simples de croissance \(\leq 1\). (Classification of simple graded Lie algebras of growth \(\leq 1)\)
cites work: Simply Connected Homogeneous Spaces
cites work: DECOMPOSITIONS OF REDUCTIVE LIE GROUPS
cites work: Q4284481
cites work: Q3998356
cites work: A classification of irreducible prehomogeneous vector spaces and their relative invariants
full work available at URL: https://doi.org/10.1007/bf02885680
OpenAlex ID: W2040271907
description: scientific article; zbMATH DE number 1036724