Possible central extensions of non-relativistic conformal algebras in 1+1
TLDR
In this paper, the authors investigated the possibility of central extension for non-relativistic conformal algebras in 1+1 dimension, and three different forms of charges can be suggested.Abstract:
We investigate possibility of central extension for non-relativistic conformal algebras in 1+1 dimension. Three different forms of charges can be suggested. A trivial charge for temporal part of the algebra exists for all elements of l-Galilei algebra class. In attempt to find a central extension as of conformal Galilean algebra for other elements of the l-Galilei class, possibility for such extension was excluded. For integer and half integer elements of the class, we can have an infinite extension of the generalized mass charge for the Virasoro-like extended algebra. For finite algebras, a regular charge inspired by Schrodinger central extension is possible.read more
Citations
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Dynamical realizations of N=1 l-conformal Galilei superalgebra
Ivan Masterov,Ivan Masterov +1 more
TL;DR: In this paper, a free N = 1 superparticle which is governed by higher derivative equations of motion and an N=1 supersymmetric Pais-Uhlenbeck oscillator for a particular choice of its frequencies is proposed.
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2D Galilean field theories with anisotropic scaling
TL;DR: In this article, the authors studied two-dimensional Galilean field theories with global translations and anisotropic scaling symmetries, and showed that such theories have enhanced local symmets, generated by the infinite dimensional spin-and-ensuremath{\ell}$ Galilean algebra with possible central extensions.
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Higher-derivative mechanics with N=2l-conformal Galilei supersymmetry
TL;DR: In this article, the analysis previously developed in [J. Math. Phys. 55 102901 (2014)] is used to construct systems which hold invariant under N = 2l-conformal Galilei superalgebra.
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Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry
TL;DR: In this paper, the analysis previously developed in [J. Math. Phys. 55 (2014) 102901] is used to construct systems which hold invariant under N = 2 l-conformal Galilei superalgebra.
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On Casimir operators of conformal Galilei algebras
TL;DR: Alshammari et al. as discussed by the authors introduced an algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras and applied the algorithm to several classes of finite dimensional conformal Galilei algesbras with central extension.
References
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