Generalised Bargmann Superalgebras
arXiv:2010.01894
Abstract
The Bargmann algebra and centrally-extended Newton-Hooke algebras describe the non-relativistic symmetries of massive particles in flat and curved spacetimes, respectively. These three algebras all arise as deformations of the universal central-extension of the static kinematical Lie algebra. In this paper, we classify the N=1 super-extensions for each of these algebras in (3+1)-dimensions, up to isomorphism. We then identify the non-empty branches of the algebraic variety describing the N=2 super-extensions of these algebras. We find 9 isomorphism classes in the N=1 case and 22 branches in the N=2 case. We then give a brief discussion on some applications of these Lie superalgebras, including their possible uses for non-relativistic supergravity and holography.
51 pages, 8 tables
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