Polynomial super-gl(n) algebras

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dc.creatorJarvis, P. D.
dc.creatorRudolph, G.
dc.date2003-01-26
dc.date2003-02-15
dc.date.accessioned2026-07-07T10:49:33Z
dc.date.available2026-07-07T10:49:33Z
dc.descriptionWe introduce a class of finite dimensional nonlinear superalgebras $L = L_{\bar{0}} + L_{\bar{1}}$ providing gradings of $L_{\bar{0}} = gl(n) \simeq sl(n) + gl(1)$. 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 $Q_{a}, \bar{Q}{}^{b}$, and even generators ${E^{a}}_{b}$, $a,b = 1,...,n$, 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 be 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 space-time supersymmetry, are discussed.
dc.description31 pages, LaTeX, including minor corrections to equation (3) and reference [60]
dc.identifierhttps://arxiv.org/abs/hep-th/0301209
dc.identifierhttp://arxiv.org/abs/hep-th/0301209
dc.identifierJ.Phys.A36:5531-5556,2003
dc.identifierdoi:10.1088/0305-4470/36/20/311
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184255
dc.subjectHigh Energy Physics - Theory
dc.titlePolynomial super-gl(n) algebras
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