Reflexive equivalence and reflexive-minimal algebras
Let $A$ be a finite-dimensional algebra over a field. A finite-dimensional algebra $B$ over the same field is called reflexively equivalent to $A$ if their categories of reflexive modules are equivalent. We prove that there is a basic algebra $A_{\min}$, unique up to isomorphism, such that $B$ is reflexively equivalent to $A$ if and only if $B\cong\operatorname{End}_{A_{\min}}(A_{\min}\oplus X)$ for some reflexive $A_{\min}$-module $X$. Moreover, we compute $A_{\min}$ explicitly. We extend these results to module-finite algebras over henselian local rings of dimension at most one under a…
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