The higher rank Virasoro algebras
type: Item
instance of: scholarly article
title: The higher rank Virasoro algebras
zbMATH Open document ID: 0733.17013
DOI: 10.1007/BF02096787
published in: Communications in Mathematical Physics
publication date: 1991-01-01T00:00:00Z
review text: The generalized Virasoro algebra V(M/F) as central extension of the Lie algebra L(M/F) is studied, where F denotes a field of arbitrary characteristic and M is a finite submodule of F. The additive orderings of M are used to study the structure and the representations of the generalized Virasoro algebras in the case of characteristic zero. Every additive ordering gives rise to a triangular decomposition of V(M/F). The automorphism group is characterized as a semidirect product (Theorem 3). The finite dimensional subalgebras are listed (Theorem 4). Verma modules and unitary Verma representation spaces are defined in the case that M is a vector lattice in the complex plane. There are six examples illustrating the considerations.
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 4212280
zbMATH Keywords: generalized Virasoro algebra
zbMATH Keywords: additive orderings
zbMATH Keywords: structure
zbMATH Keywords: representations
zbMATH Keywords: characteristic zero
zbMATH Keywords: automorphism group
zbMATH Keywords: finite dimensional subalgebras
zbMATH Keywords: Verma modules
author: Jiří Patera
author: H. Zassenhaus
reviewed by: Helmut Boseck
MaRDI profile type: Publication
cites work: Über Wittsche Lie-Ringe
cites work: Q3820760
cites work: On Lie gradings. I
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cites work: Q3974917
cites work: The Representations of Lie Algebras of Prime Characteristic
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description: scientific article; zbMATH DE number 4212280