Resumen de Koszul properties of the moment map of some classical representations

Aldo Conca , Hans Christian Herbig, Srikanth B. Iyengar

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