## arXiv Analytics

### arXiv:1112.0634 [math-ph]AbstractReferencesReviewsResources

#### Galilean conformal algebras in two spatial dimension

Published 2011-12-03, updated 2014-08-14Version 2

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 immediately that the Verma modules are irreducible for nonvanishing highest weights. It is also shown that the Verma modules are reducible for vanishing highest weights. For half-integer \ell it is shown that all the Verma module is reducible. These results are independent of the central charges.

Comments: 21 pages, Major revision. Erorr in Theorem 1 is corrected. More general case is investigated. New results, new references
Categories: math-ph, hep-th, math.MP
Related articles: Most relevant | Search more
arXiv:physics/9801008 [math-ph] (Published 1998-01-08)
Central extensions of the families of quasi-unitary Lie algebras
arXiv:1212.6288 [math-ph] (Published 2012-12-27, updated 2013-01-04)
Some representations of planar Galilean conformal algebra
arXiv:1902.05741 [math-ph] (Published 2019-02-15)
$\mathbb{Z}_2 \times \mathbb{Z}_2$ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions