Cohomology of Noncommutative Hilbert Schemes

Dedicated to Claus Michael Ringel on the occasion of his sixtieth birthday


Noncommutative Hilbert schemes, introduced by M. V. Nori, parametrize left ideals of finite codimension in free algebras. More generally, parameter spaces of finite-codimensional submodules of free modules over free algebras are considered. Cell decompositions of these varieties are constructed, whose cells are parametrized by certain types of forests. Asymptotics for the corresponding Poincaré polynomials and properties of their generating functions are discussed.

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Correspondence to Markus Reineke.

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Mathematics Subject Classifications (2000)

Primary: 16G20; secondary: 14D20.

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Reineke, M. Cohomology of Noncommutative Hilbert Schemes. Algebr Represent Theor 8, 541–561 (2005).

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  • representations of free algebras
  • moduli of representations
  • Hilbert schemes
  • Betti numbers