The Poisson cohomology of $\mathfrak{sl}^{\ast}_2 (\mathbb{R})$

We compute the smooth Poisson cohomology of the linear Poisson structure associated with the Lie algebra $\mathfrak{sl}_2 (\mathbb{R})$, or equivalently, the Lie algebra cohomology of $\mathfrak{sl}_2 (\mathbb{R})$ with coefficients $C^\infty (\mathfrak{sl}^{\ast}_2 (\mathbb{R}))$.

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Received 11 February 2022

Accepted 27 November 2022

Published 22 December 2023