We prove that deformations of tame Krull-Schmidt bimodule problems with trivial differential are again tame. Here we understand deformations via the structure constants of the projective realizations which may be considered as elements of a suitable variety. We also present some applications to the representation theory of vector space categories which are a special case of the above bimodule problems.
We classify the irreducible components of varieties of modules over tubular algebras. Our results are stated in terms of root combinatorics. They can be applied to understand the varieties of modules over the preprojective algebras of Dynkin type 𝔸₅ and 𝔻₄.
The main aim of the paper is to classify the discrete derived categories of bounded complexes of modules over finite dimensional algebras.
Let be a preprojective algebra of type , and let be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories for an injective -module, and we introduce a mutation operation between complete rigid modules in . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to .
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