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.
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Supported by National Natural Science Foundation of China (Grant No. 11271056), Jiangsu Overseas Research & Training Program for University Prominent Young & Middle-aged Teachers and Presidents, and the Fundamental Research Funds for the Central Universities
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Wu, Y.Z., Yue, X.Q. & Zhu, L.S. Cohomology of the Schrödinger algebra S(1). Acta. Math. Sin.-English Ser. 30, 2054–2062 (2014). https://doi.org/10.1007/s10114-014-3743-x
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DOI: https://doi.org/10.1007/s10114-014-3743-x