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arXiv · 1705.02688

Koszul properties of the moment map of some classical representations

Aldo Conca·Hans-Christian Herbig·Srikanth B. Iyengar
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Abstract

This work concerns the moment map $\mu$ associated with the standard representation of a classical Lie algebra. For applications to deformation quantization it is desirable that $S/(\mu)$, the coordinate algebra of the zero fibre of $\mu$, be Koszul. The main result is that this algebra is not Koszul for the standard representation of $\mathfrak{sl}_{n}$, and of $\mathfrak{sp}_{n}$. This is deduced from a computation of the Betti numbers of $S/(\mu)$ as an $S$-module, which are of interest also from the point of view of commutative algebra.

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Aldo Conca, Hans-Christian Herbig, Srikanth B. Iyengar. 2017-05-07. Koszul properties of the moment map of some classical representations. https://arxiv.org/abs/1705.02688

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