Representations as Elements in Affine Composition Algebras
نویسنده
چکیده
Let A be the path algebra of a Euclidean quiver over a finite field k. The aim of this paper is to classify the modules M with the property [M ] ∈ C(A), where C(A) is Ringel’s composition algebra. Namely, the main result says that if |k| 6= 2, 3, then [M ] ∈ C(A) if and only if the regular direct summand of M is a direct sum of modules from non-homogeneous tubes with quasi-dimension vectors non-sincere. The main methods are representation theory of affine quivers, the structure of triangular decompositions of tame composition algebras, and the invariant subspaces of skew derivations. As an application, we see that C(A) = H(A) if and only if the quiver of A is of Dynkin type.
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