A new class of infinite-dimensional Lie algebras: an analytical continuation of the arbitrary finite-dimensional semisimple Lie algebra
type: Item
instance of: scholarly article
zbMATH Open document ID: 0968.17503
DOI: 10.1142/S021773239000130X
published in: Modern Physics Letters A
publication date: 2001-08-05T00:00:00Z
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 81T10
zbMATH DE Number: 1630713
Wikidata QID: Q115246431
author: Efim Samoĭlovich Fradkin
author: V. Ya. Linetsky
MaRDI profile type: Publication
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title: A new class of infinite-dimensional Lie algebras: an analytical continuation of the arbitrary finite-dimensional semisimple Lie algebra
review text: The authors construct for any semisimple finite-dimensional Lie algebra \(\mathfrak g\) a unique infinite-dimensional Lie algebra \(\text{AC}(\mathfrak g)\) which is an analytic continuation of \(\mathfrak g\) from its root system to the root lattice. They show that each finite-dimensional irreducible representation of \(\mathfrak g\) has a unique analytic continuation to an infinite-dimensional representation of \(\text{AC}(\mathfrak g)\). As special cases, they give the Poisson bracket realizations of \(\text{AC}(\mathfrak g)\) for the simple finite-dimensional Lie algebras of the classical series, the analytic continuation of the Lie superalgebra \(\text{osp}(1|2n)\), and higher spin algebras. The case \(\mathfrak g=\text{sp}_2\) gives the Virasoro algebra. The authors believe that the proposed theory may be an algebraic basis for exactly solvable \(D\)-dimensional quantum models.
reviewed by: Alice Fialowski
description: scientific article; zbMATH DE number 1630713