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A representation theoretic study of noncommutative symmetric algebras. (arXiv:1710.05868v2 [math.AG] UPDATED)

来源于:arXiv
We study Van den Bergh's noncommutative symmetric algebra $\mathbb{S}^{nc}(M)$ (over division rings) via Minamoto's theory of Fano algebras. In particular, we show $\mathbb{S}^{nc}(M)$ is coherent, and its proj category $\mathbb{P}^{nc}(M)$ is derived equivalent to the corresponding bimodule species. This generalizes the main theorem of \cite{minamoto}, which in turn is a generalization of Beilinson's derived equivalence. As corollaries, we show that $\mathbb{P}^{nc}(M)$ is hereditary and there is a structure theorem for sheaves on $\mathbb{P}^{nc}(M)$ analogous to that for $\mathbb{P}^1$. 查看全文>>