Cohomological Rigidity of the Schrodinger Algebra S(N) and its Central Extension S(N)

摘要

It is shown that for any N not equal 2, the Schrodinger algebra S(N) and its central extension (S) over cap (N) are cohomologically rigid Lie algebras, i.e., have a vanishing second Chevalley cohomology group with values in the adjoint representation. Further, it is shown that the main cohomological difference between these algebras lies in the structure of the third cohomology space.