Affine superalgebras, unitary representations and the Sugawara construction

DOI10.1016/0550-3213(89)90518-XzbMath0689.17023OpenAlexW2090812276MaRDI QIDQ581651

Peter D. Jarvis, Ruibin Zhang

Publication date: 1989

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0550-3213(89)90518-x

zbMATH Keywords

highest weight representationsLie superalgebrasVirasoro central chargeKac-Moody central extensionSugawara construction

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Supersymmetric field theories in quantum mechanics (81T60) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Superalgebras (17A70) Graded Lie (super)algebras (17B70)

Related Items (3)

Sugawara-type constructions of the Virasoro algebra based on the twisted affine Kac–Moody superalgebras ⋮ Integrable representations of affine \(A(m,n)\) and \(C(m)\) superalgebras ⋮ Vertex operator superalgebras associated with affine Lie superalgebras

Cites Work

• Operator content of two-dimensional conformally invariant theories
• Unitary representations of noncompact supergroups
• Superalgebras, symplectic bosons and the Sugawara construction
• Formal relations between classical superalgebras and fermion–boson creation and annihilation operators
• Hermitean Oscillator-like Realizations of Classical Algebras and Superalgebras in Hilbert Space with Positive Definite Metric
• KAC-MOODY AND VIRASORO ALGEBRAS IN RELATION TO QUANTUM PHYSICS
• Classification of real simple Lie superalgebras of classical type
• Representations of Osp(2, 1) and the metaplectic representation
• Graded Lie algebras: Generalization of Hermitian representations

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