In this paper we study the second cohomology space for the n-th Schr\"{o}dinger algebra schₙ. We prove that the second cohomology space is vanishing for n ≥ 3 and show that (H²(sch₂, sch₂)) =2. Moreover, we investigate the factor algebra of the Schr\"{o}dinger algebra by its center and determine the second cohomology group of this factor algebra.
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Jumaniyozov et al. (2024) studied this question.
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