Galilean conformal algebras in two spatial dimension

@article{Aizawa2011GalileanCA,
  title={Galilean conformal algebras in two spatial dimension},
  author={Naruhiko Aizawa and Yuta Kimura},
  journal={arXiv: Mathematical Physics},
  year={2011}
}
A class of infinite dimensional Galilean conformal algebra in (2+1) dimensional spacetime is studied. Each member of the class, denoted by \alg_{\ell}, is labelled by the parameter \ell. The parameter \ell takes a spin value, i.e., 1/2, 1, 3/2, .... We give a classification of all possible central extensions of \alg_{\ell}. Then we consider the highest weight Verma modules over \alg_{\ell} with the central extensions. For integer \ell we give an explicit formula of Kac determinant. It results… 

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