Block-diagonalization of matrices over local rings.II
Dmitry Kerner
TL;DR
This paper extends criteria for block-diagonalizing matrices over local rings to the decomposability of quiver representations, broadening the understanding of matrix and representation decomposability over local rings.
Contribution
It generalizes previous criteria from matrices to quiver representations over local rings, providing new conditions for their decomposability.
Findings
Extended block-diagonalization criteria to quiver representations.
Provided algebraic conditions for decomposability over local rings.
Connected matrix decomposability with quiver representation theory.
Abstract
Consider rectangular matrices over a local ring R. In the previous work we have obtained criteria for block-diagonalization of such matrices, i.e. U A V=A_1\oplus A_2, where U,V are invertible matrices over R. In this short note we extend the criteria to the decomposability of quiver representations over R.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Commutative Algebra and Its Applications