Infinitesimal deformations and central extensions of the n-th Schr¨odinger algebra

In this paper, we determine the infinitesimal deformations of the n-th Schr¨odinger algebra schn and its factor algebra gn by the one-dimensional center. More precisely, we prove that the second cohomology groups of schn and gn with values in the adjoint representations vanish for n ≥ 3: On the other hand, it is shown that for n = 2 in both cases this cohomology space is onedimensional. Moreover, compute the second cohomology groups of schn and gn with values in the trivial representation.