A Representation Theoretic Study of Non-Commutative Symmetric Algebras. Issue 3 (14th February 2019) - Chan, D.; Nyman, A.
Abstract: We study Van den Bergh's non-commutative symmetric algebra 𝕊 nc ( M ) (over division rings) via Minamoto's theory of Fano algebras. In particular, we show that 𝕊 nc ( M ) is coherent, and its proj category ℙ nc ( M ) is derived equivalent to the corresponding bimodule species. This generalizes the main theorem of [8], which in turn is a generalization of Beilinson's derived equivalence. As corollaries, we show that ℙ nc ( M ) is hereditary and there is a structure theorem for sheaves on ℙ nc ( M ) analogous to that for ℙ 1 .