Possible Central Extensions of Non-Relativistic Conformal Algebras in 1+1

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 CGA 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 Schr\"odinger central extension is possible.