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Journal of Lie Theory 27 (2017), No. 2, 315--328
Copyright Heldermann Verlag 2017

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

Rutwig Campoamor-Stursberg
Instituto de Matemática Interdisciplinar, Fac. CC. Matemáticas, Universidad Complutense, Plaza de Ciencias 3, 28040 Madrid, Spain


It is shown that for any $N\neq 2$, the Schr\"odinger algebra $S(N)$ and its central extension $\widehat{S}(N)$ 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.

Keywords: Rigidity, Chevalley cohomology, Schroedinger algebra, Lie algebras.

MSC: 17B10, 17B56

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