Lowest weight representations of super Schrödinger algebras in low dimensional spacetime

Aizawa, N.

doi:10.1088/1742-6596/284/1/012007

Cited by 3 publications

(3 citation statements)

References 59 publications

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“…We give a realization of the super-GCA in section 5. However, more mathematical works such as classification of irreducible representations (see [33,34] for = 1/2) should be performed for further understanding and physical applications of super-GCA.…”

Section: Discussionmentioning

confidence: 99%

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$ \mathcal{N} = 2$ Galilean superconformal algebras with a central extension

Aizawa¹

2012

J. Phys. A: Math. Theor.

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N = 2 Supersymmetric extensions of Galilean conformal algebra (GCA), specified by spin ℓ and dimension of space d, are investigated. Duval and Horváthy showed that the ℓ = 1/2 GCA has two types of supersymmetric extensions, called standard and exotic. Recently, Masterov intorduced a centerless super-GCA for arbitrary ℓ wchich corresponds to the standard extension. We show that the Masterov's super-GCA has two types of central extensions depending on the parity of 2ℓ. We then introduced a novel super-GCA for arbitrary ℓ corresponding to the exotic extension. It is shown that the exotic superalgebra also has two types of central extensions depending on the parity of 2ℓ. Furthermore, we give a realization of the standard and exotic super-GCA's in terms of their subalgebras. Finally, we present a N = 1 supersmmetric extension of GCA with central extensions.

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Section: Discussionmentioning

confidence: 99%

“…Previous to [17] there were some works on = 1/2 super-GCA [18][19][20][21]. These works are followed by a recent active study on physical and mathematical aspects of = 1/2 superalgebra [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

$ \mathcal{N} = 2$ Galilean superconformal algebras with a central extension

Aizawa¹

2012

J. Phys. A: Math. Theor.

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“…It is known that the representation theory of super Schrödinger algebras play fundamental roles in classifying non-relativistic superconformal field theories. The N = 1 super Schrödinger algebra in (1 + 1)-dimensional spacetime is defined to be Lie superalgebra: S = S(1 | 1) = S0 ⊕ S1, where the even part S0 = span C {e, f, h, p, q, z} is the Schrödinger algebra: Aizawa [1,2] investigated the Verma modules of super Schrödinger algebras in low dimensional spacetime. And other researchers in [21] studied the simple weight modules over S. However, it seems that the supermodules (A left S-supermodules is a supervector space V which is a left S-module in the usual sense such that S θ V τ ⊆ V θ+τ for θ, τ ∈ Z/2Z ) for this Lie superalgebra are not studied well.…”

Section: Introductionmentioning

confidence: 99%

Simple Harish-Chandra supermodules over the super Schrödinger algebra

2015

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We study the N = 1 super Schrödinger algebra S in (1 + 1)-dimensional spacetime. The first part of this paper determines the necessary and sufficient conditions for highest weight supermodules over S to be simple. The paper also describes the structure of all Verma supermodules and determines all simple Harish-Chandra supermodules over S. Keywordssuper Schrödinger algebra, weight supermodule, simple supermodule, Harish-Chandra supermodules MSC(2010) 17B10, 17B65, 17B68Citation: Cai Y A, Gao Y, Wang Y J. Simple Harish-Chandra supermodules over the super Schrödinger algebra.

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Simple Harish-Chandra modules over super Schrödinger algebra in (1+1) dimensional spacetime

Zhang

Cai

Wang

2014

Journal of Mathematical Physics

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The N = 1 super Schrödinger algebra \documentclass[12pt]{minimal}\begin{document}$\mathcal {S}(1|1)$\end{document}S(1|1) in (1+1) dimensional spacetime contains a subalgebra isomorphic to \documentclass[12pt]{minimal}\begin{document}$\mathfrak {osp}(1|2)$\end{document}osp(1|2)-module. Let V be a simple weight module for the N = 1 super Schrödinger algebra \documentclass[12pt]{minimal}\begin{document}$\mathcal {S}(1|1)$\end{document}S(1|1) but not a simple \documentclass[12pt]{minimal}\begin{document}$\mathfrak {osp}(1|2)$\end{document}osp(1|2)-module. Let ω ∈ supp(V). If V is neither a highest weight module nor a lowest weight module for \documentclass[12pt]{minimal}\begin{document}$\mathcal {S}(1|1)$\end{document}S(1|1), we prove that \documentclass[12pt]{minimal}\begin{document}$\mathrm{supp}(V)=\omega +\mathbb {Z}$\end{document} supp (V)=ω+Z, and all non-trivial weight spaces of V have the same dimension. We prove that if V is a Harish-Chandra module, then it is a highest weight module, or lowest weight module, or a twisted localization of a highest weight module.

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Lowest weight representations of super Schrödinger algebras in low dimensional spacetime

Cited by 3 publications

References 59 publications

$ \mathcal{N} = 2$ Galilean superconformal algebras with a central extension

$ \mathcal{N} = 2$ Galilean superconformal algebras with a central extension

Simple Harish-Chandra supermodules over the super Schrödinger algebra

Simple Harish-Chandra modules over super Schrödinger algebra in (1+1) dimensional spacetime

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