Invariant Theory of Canonical Algebras

✍ Scribed by Mátyás Domokos; Helmut Lenzing

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 188 KB
• Volume: 228
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8298

✦ Synopsis

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 Ž 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.