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Polynomial super-gl(n) algebras


Jarvis, PD and Rudolph, G, Polynomial super-gl(n) algebras, Journal of Physics A: Mathematical and General, 36, (20) pp. 5531-5555. ISSN 0305-4470 (2003) [Refereed Article]

DOI: doi:10.1088/0305-4470/36/20/311


We introduce a class of finite-dimensional nonlinear superalgebras L = L0̄? + L1̄ providing gradings of L 0̄ = gl(n) ≃ sl(n) + gl(1). Odd generators close by anticommutation on polynomials (of degree >1) in the gl(n) generators. Specifically, we investigate 'type I' super-gl(n) algebras, having odd generators transforming in a single irreducible representation of gl(n) together with its contragredient. Admissible structure constants are discussed in terms of available gl(n) couplings, and various special cases and candidate superalgebras are identified and exemplified via concrete oscillator constructions. For the case of the n-dimensional defining representation, with odd generators Qa, Q̄b and even generators E ab, a, b = 1,...,n, a three-parameter family of quadratic super-gl(n) algebras (deformations of sl(n/1)) is defined. In general, additional covariant Serre-type conditions are imposed in order that the Jacobi identities are fulfilled. For these quadratic super-gl(n) algebras, the construction of Kac modules and conditions for atypicality are briefly considered. Applications in quantum field theory, including Hamiltonian lattice QCD and spacetime supersymmetry, are discussed.

Item Details

Item Type:Refereed Article
Research Division:Physical Sciences
Research Group:Other physical sciences
Research Field:Other physical sciences not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the physical sciences
UTAS Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:28442
Year Published:2003
Web of Science® Times Cited:8
Deposited By:Physics
Deposited On:2003-08-01
Last Modified:2010-06-10

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