Koszul properties of the moment map of some classical representations

• Autores: Aldo Conca , Hans Christian Herbig, Srikanth B. Iyengar
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 69, Fasc. 3, 2018, págs. 337-357
• Idioma: inglés
• DOI: 10.1007/s13348-018-0226-x
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• Resumen

  • 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.