On the classification of subalgebras of \(\text{Cend}_N\) and \(\text{gc}_N\).
type: Item
instance of: scholarly article
title: On the classification of subalgebras of \(\text{Cend}_N\) and \(\text{gc}_N\).
zbMATH Open document ID: 1034.17018
DOI: 10.1016/S0021-8693(02)00632-4
author: Carina Boyallian
author: Victor G. Kac
author: Jose I. Liberati
published in: Journal of Algebra
publication date: 2003-04-28T00:00:00Z
review text: The authors classify all infinite subalgebras of the conformal algebras \(\text{Cend}_{N}\) and \(\text{gc}_{N}\) over the field \(\mathbb C\) (these algebras are direct `conformal' analogues of the matrix algebras \(M_N(\mathbb C)\) and \(\text{gl}_N (\mathbb C)\), respectively). For the definition of conformal algebra, see \textit{V. G. Kac}, Vertex algebras for beginners. 2nd ed. University Lecture Series. 10. Providence, RI: American Mathematical Society (AMS) (1998; Zbl 0924.17023). They describe all finite irreducible modules over \(\text{Cend}_{N,P}\). The authors also describe all automorphisms of \(\text{Cend}_{N,P}\) and classify all homomorphisms and anti-homomorphisms of \(\text{Cend}_{N,P}\) to \(\text{Cend}_{N}\) .
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 17B81
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 1901816
zbMATH Keywords: conformal algebras
zbMATH Keywords: classification
zbMATH Keywords: automorphisms
zbMATH Keywords: analogue of Burnside theorem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1901816