- TitleOn minimal disjoint degenerations with preprojective and preinjective direct summands over tame path algebras / vorgelegt von Guido Frank
- Institutional NoteWuppertal, Univ., Diss., 2008
- Document typeDissertation (PhD)
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We consider finite-dimensional modules over tame path algebras and study the 'building blocks' of their degenerations. These are the minimal disjoint degenerations to the direct sum of two indecomposables U, V. For the building blocks, we derive a reduction theorem that holds if U or V are non-regular. Subsequently we focus on minimal degenerations to the direct sum of a preprojective and a preinjective indecomposable and use the reduction theorem to introduce a new method to analyze the codimensions of this sort of degenerations. We show that the codimensions are bounded. By means of computer calculations we determine this bound explicitly. The codimension is always one. Finally, this leads to a minimality preserving periodicity theorem, which reduces the classification of the building blocks to a finite problem.
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