Infinite rank representations of orders in nonsemisimple algebras, and module categories

W. Rump

University of Stuttgart

Abstract: Let $R$ be a Dedekind domain with quotient field $K$ and let $\Lambda$ be an $R$-order in a finite-dimensional $K$-algebra $A$ such that $A/\operatorname{Rad}A$ is separable. We show that if $A$ is not semisimple, then there exists a maximal $R$-order $\Delta$ in a skew-field such that the category $\Lambda\text{-}\mathbf{Lat}$ of $R$-projective $\Lambda$-modules admits a full module category $\Delta\text{-}\mathbf{Mod}$ as a subfactor.

UDC: 512.583

 English version: Journal of Mathematical Sciences (New York), 2007, 144:2, 3993–4003

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