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A Representation Theoretic Study of Non-Commutative Symmetric Algebras

Published online by Cambridge University Press:  14 February 2019

D. Chan
Affiliation:
University of New South Wales, Sydney, NSW, Australia ([email protected])
A. Nyman
Affiliation:
Western Washington University, Bellingham, WA, USA ([email protected])

Abstract

We study Van den Bergh's non-commutative symmetric algebra 𝕊nc(M) (over division rings) via Minamoto's theory of Fano algebras. In particular, we show that 𝕊nc(M) is coherent, and its proj category ℙnc(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 ℙnc(M) is hereditary and there is a structure theorem for sheaves on ℙnc(M) analogous to that for ℙ1.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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