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Triangular decomposition of the composition algebra of \(\widetilde A_{11}\). (Chinese. English summary) Zbl 0903.16011

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
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