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A class of quadratic deformations of Lie superalgebras


Jarvis, PD and Rudolph, G and Yates, LA, A class of quadratic deformations of Lie superalgebras, Journal of Physics A: Mathematical and Theoretical, 44, (23) Article 235205. ISSN 1751-8113 (2011) [Refereed Article]

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Copyright © 2011 Institute of Physics

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DOI: doi:10.1088/1751-8113/44/23/235205


We study certain Z2-graded, finite-dimensional polynomial algebras of degree 2 which are a special class of deformations of Lie superalgebras, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalized Jacobi relations in the context of the Koszul property, and give a proof of the Poincar´e–Birkhoff–Witt basis theorem. We give several concrete examples of quadratic Lie superalgebras for low-dimensional cases, and discuss aspects of their structure constants for the ‘type I’ class. We derive the equivalent of the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate in detail one specific case, the quadratic generalization gl2(in/i/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Mathematical physics
Research Field:Algebraic structures in mathematical physics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the physical sciences
UTAS Author:Jarvis, PD (Dr Peter Jarvis)
UTAS Author:Yates, LA (Mr Luke Yates)
ID Code:69825
Year Published:2011
Web of Science® Times Cited:5
Deposited By:Mathematics and Physics
Deposited On:2011-05-20
Last Modified:2017-08-25

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