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arXiv · 2407.07435

Infinitesmal deformations and central extensions of the $n$-th Schr\"odinger algebra

Doston Jumaniyozov·Surayyo Sheraliyeva
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Abstract

In this paper we study the second cohomology space for the $n$-th Schr\"{o}dinger algebra $\mathfrak{sch}_n$. We prove that the second cohomology space is vanishing for $n \geq 3$ and show that $\dim(H^2(\mathfrak{sch}_2, \mathfrak{sch}_2)) =2.$ 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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Doston Jumaniyozov, Surayyo Sheraliyeva. 2024-07-10. Infinitesmal deformations and central extensions of the $n$-th Schr\"odinger algebra. https://arxiv.org/abs/2407.07435

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