Invariant Theory of Canonical Algebras

Abstract

Based on the first fundamental theorem of classical invariant theory we present a reduction technique for computing relative invariants for quivers with relations. This is applied to the invariant theory of canonical algebras and yields an explicit construction of the moduli spaces (together with the quotient morphisms from the corresponding representation spaces) for families of modules with a fixed dimension vector belonging to the central sincere separating subcategory. By means of a tilting process we extend these results to the invariant theory of concealed-canonical algebras, thus covering the cases of tame hereditary, tame concealed, and tubular algebras, respectively. Our approach yields, in particular, a uniform treatment to an essential part of the invariant theory of extended Dynkin quivers, a topic popular over the years, but stretches far beyond since also concealed-canonical algebras of tubular or wild representation type are covered.