Cohomology of the Schrödinger algebra S(1)

Abstract

We explicitly compute the first and second cohomology groups of the Schrödinger algebra S(1) with coefficients in the trivial module and the finite-dimensional irreducible modules. We also show that the first and second cohomology groups of S(1) with coefficients in the universal enveloping algebras U (S(1)) (under the adjoint action) are infinite dimensional.

New examples of infinite-dimensional n-Lie algebras

“…For example, all derivations of the Schrödinger algebra determined and it is shown that this algebra admits an outer derivation (see [22]). Moreover, the first and second cohomology groups of the Schrödinger algebra in (1 + 1)-dimensional space time, with coefficients in the trivial module and the finite-dimensional irreducible modules are computed [21]. The adjoint cohomology and central extension of the Schrödinger algebra in (n + 1)-dimensional space time, are investigated in [6].…”