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A noncommutative version of Beilinson's Theorem

Hiroyuki Minamoto
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Abstract

We prove that the category of representations of the N-Kronecker quiver and that of coherent sheaves on the noncommutative projective scheme of $R=k< X_1,...,X_N >/(\sum^N_{i=1}X_i^2)$ are derived equivalent. This equivalence is easily proved by applying Orlov's Theorem, on the other hand,in our proof,the quadratic relation $\sum_{i=1}^NX_i^2$ naturally arises from Auslander-Reiten Theory.

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Hiroyuki Minamoto. 2007-09-09. A noncommutative version of Beilinson's Theorem. https://arxiv.org/abs/math/0702861

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