3 years ago

# Koszul properties of the moment map of some classical representations

Aldo Conca, Hans-Christian Herbig, Srikanth B. Iyengar

### 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.

Open URL: http://arxiv.org/pdf/1705.02688

DOI: 10.1007/s13348-018-0226-x

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