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Indecomposable Modules for Domestic Canonical Algebras in Arbitrary Characteristic

Sylwia Komoda, Hagen Meltzer

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Abstract

We describe explicitly all indecomposable modules of rank 6 over a domestic canonical algebra of quiver type over a field k of arbitrary characteristic. Together with the results given in (5) this yields an explicit de- scription of all preprojective and preinjective indecomposable modules (and of all indecomposable modules if k is algebraically closed) for a domestic canon- ical algebra of quiver type. In particular for those algebras each preprojective and each preinjective indecomposable module can be represented by matrices whose coefficients are 0 and 1.

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We describe explicitly all indecomposable modules of rank 6 over a domestic canonical algebra of quiver type over a field k of arbitrary characteristic. Together with the results given in (5) this yields an explicit de- scription of all preprojective and preinjective indecomposable modules (and of all indecomposable modules if k is algebraically closed) for a domestic canon- ical algebra of quiver type. In particular for those algebras each preprojective and each preinjective indecomposable module can be represented by matrices whose coefficients are 0 and 1.

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Available abstract

We describe explicitly all indecomposable modules of rank 6 over a domestic canonical algebra of quiver type over a field k of arbitrary characteristic. Together with the results given in (5) this yields an explicit de- scription of all preprojective and preinjective indecomposable modules (and of all indecomposable modules if k is algebraically closed) for a domestic canon- ical algebra of quiver type. In particular for those algebras each preprojective and each preinjective indecomposable module can be represented by matrices whose coefficients are 0 and 1.

Key concepts: Indecomposable module, Quiver, Algebraically closed field, Mathematics, Pure mathematics, Rank (graph theory), Algebra over a field, Field (mathematics)

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