Zhang, Shunhua Triangular decomposition of the composition algebra of \(\widetilde A_{11}\). (Chinese. English summary) Zbl 0903.16011 Acta Math. Sci. (Chin. Ed.) 18, No. 1, 11-18 (1998). Summary: Let \(A\) be the hereditary algebra of type \(\widetilde A_{11}\) over a finite field, \({\mathcal H}(A)\) and \(C(A)\) be respectively the Ringel-Hall algebra and the composition algebra. It is proved that \(C(A)={\mathcal P}\cdot{\mathcal T}\cdot{\mathcal I}\), where \(\mathcal P\) (resp. \(\mathcal I\)) is the subalgebra of \(C(A)\) generated by the preprojective (resp. preinjective) \(A\)-modules, and \(\mathcal T\) is the subalgebra generated by the regular elements of \(C(A)\). MSC: 16G30 Representations of orders, lattices, algebras over commutative rings 16D90 Module categories in associative algebras Keywords:preprojective modules; preinjective modules; hereditary algebras; Ringel-Hall algebras; composition algebras PDFBibTeX XMLCite \textit{S. Zhang}, Acta Math. Sci. (Chin. Ed.) 18, No. 1, 11--18 (1998; Zbl 0903.16011)