Triangular Decomposition of Tame Non-Simply Laced Composition Algebras

AbstractLet A be a finite dimensional hereditary algebra over a finite field, and let C(A) be the composition algebra of A. Let P (resp. I) be the subalgebra of C(A) generated by the preprojective (resp. preinjective) A-modules, and let T be the subalgebra generated by rd, where rd=∑[M]∈H(A),[M] runs over the isomorphism classes of the regular A-modules with dimension vector d, and H(A) is the Ringel–Hall algebra of A. Then we prove that C(A)=P·T·I, if A is one of the types B̃n, C̃n, BC̃n, BD̃n, CD̃n, F̃41, F̃42, G̃21, G̃22, or Ã11