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The D-standard and K-standard categories

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arxiv 1612.06051 v2 pith:XJEHR6DF submitted 2016-12-19 math.RT math.KTmath.RA

The D-standard and K-standard categories

classification math.RT math.KTmath.RA
keywords standardmathbfcategorymodulecategoriesproveabelianadditive
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We introduce the notions of a $\mathbf{D}$-standard abelian category and a $\mathbf{K}$-standard additive category. We prove that for a finite dimensional algebra $A$, its module category is $\mathbf{D}$-standard if and only if any derived autoequivalence on $A$ is standard, that is, given by a two-sided tilting complex. We prove that if the subcategory of projective $A$-modules is $\mathbf{K}$-standard, then the module category is $\mathbf{D}$-standard. We provide new examples of $\mathbf{D}$-standard module categories.

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