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Contemporary Mathematics Volume 00, 1997

Summary: Contemporary Mathematics
Volume 00, 1997
Moduli spaces of graded representations
of finite dimensional algebras
E. Babson, B. Huisgen-Zimmermann, and R. Thomas
Abstract. Let be a basic finite dimensional algebra over an algebraically
closed field, presented as a path algebra modulo relations; further, assume
that is graded by lengths of paths. The paper addresses the classifiability,
via moduli spaces, of classes of graded -modules with fixed dimension d and
fixed top T. It is shown that such moduli spaces exist far more frequently
than they do for ungraded modules. In the local case (i.e., when T is simple),
the graded d-dimensional -modules with top T always possess a fine moduli
space which classifies these modules up to graded-isomorphism; moreover, this
moduli space is a projective variety with a distinguished affine cover that
can be constructed from quiver and relations of . When T is not simple,
existence of a coarse moduli space for the graded d-dimensional -modules
with top T forces these modules to be direct sums of local modules; under the
latter condition, a finite collection of isomorphism invariants of the modules
in question yields a partition into subclasses, each of which has a fine moduli
space (again projective) parametrizing the corresponding graded-isomorphism


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics