A Representation Theoretic Study of Non-Commutative Symmetric Algebras. Issue 3 (14th February 2019)

• Record Type: Journal Article
• Authors: Chan, D.; Nyman, A.
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 62:Issue 3(2019)
• Page Start: 875
• Page End: 887
• Publication Date: 2019-02-14
• Subjects: non-commutative algebraic geometry, -- non-commutative curve, -- non-commutative symmetric; Primary 14A22, -- 16S38, -- Secondary 16E35; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091518000871
• Languages: English
• ISSNs: 0013-0915

Abstract

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 .