Cohomology of Noncommutative Hilbert Schemes: Dedicated to Claus Michael Ringel on the occasion of his sixtieth birthday

Author: Reineke, Markus

Source: Algebras and Representation Theory, Volume 8, Number 4, October 2005 , pp. 541-561(21)

Publisher: Springer

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Abstract:

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.

Keywords: representations of free algebras; moduli of representations; Hilbert schemes; Betti numbers

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10468-005-8762-y

Affiliations: 1: Mathematisches Institut, Universität Münster, Einsteinstr. 62, D-48149, Münster, Germany, Email: reinekem@math.uni-muenster.de

Publication date: 2005-10-01