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## User: stephan-weispfenning

### Title: Properties of the fixed ring of a preprojective algebra

For a finite group acting on a polynomial ring, the Chevalley-Shephard-Todd
Theorem proves that the fixed subring is isomorphic to a polynomial ring if and
only if the group is generated by pseudo-reflections. In recent years, progress
was made in work of Kirkman, Kuzmanovich, Zhang, and others to extend this
result to regular algebras by expanding pseudo-reflections to
quasi-reflections. Naturally, the question arises if the theory generalizes
further to non-connected noncommutative algebras. Our objects of study will be
preprojective algebras which are certain factor algebras of path algebras
corresponding to extended Dynkin diagrams of type $A$, $D$ or $E$. This work
answers the question what conditions need to be satisfied by the fixed ring in
order to make a rich theory possible. On our way, we will point out additional
difficulties in establishing quasi-reflections using the trace and reveal
situations which do not occur for regular algebras.

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