Frobenius Structural Matrix Algebras
Sorin Dascalescu, Miodrag C. Iovanov, Sorina Predut

TL;DR
This paper characterizes when structural matrix algebras are Frobenius, showing they are Frobenius if and only if they are block-diagonal with full matrix blocks, based on incidence coalgebra properties.
Contribution
It provides a precise criterion for Frobenius property in structural matrix algebras using incidence coalgebra theory.
Findings
Structural matrix algebra is Frobenius iff it has a block-diagonal form with full matrix blocks.
The incidence coalgebra of a locally finite preordered set is right co-Frobenius under certain conditions.
The characterization links algebraic Frobenius property to combinatorial block structures.
Abstract
We discuss when the incidence coalgebra of a locally finite preordered set is right co-Frobenius. As a consequence, we obtain that a structural matrix algebra over a field is Frobenius if and only if it consists, up to a permutation of rows and columns, of diagonal blocks which are full matrix algebras over .
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