New York Journal of Mathematics
Volume 14 (2008) 325-378


Di Ming Lu, John H. Palmieri, Quan Shui Wu, and James J. Zhang

Koszul equivalences in A-algebras

Published: August 23, 2008
Keywords: A-algebra, graded algebra, Artin-Schelter regular algebra, Koszul duality, derived equivalence, Gorenstein property
Subject: 16A03,16A62,16E65

We prove a version of Koszul duality and the induced derived equivalence for Adams connected A-algebras that generalizes the classical Beilinson-Ginzburg-Soergel Koszul duality. As an immediate consequence, we give a version of the Bernstein-Gel'fand-Gel'fand correspondence for Adams connected A-algebras.

We give various applications. For example, a connected graded algebra A is Artin-Schelter regular if and only if its Ext-algebra ExtA(k,k) is Frobenius. This generalizes a result of Smith in the Koszul case. If A is Koszul and if both A and its Koszul dual A! are noetherian satisfying a polynomial identity, then A is Gorenstein if and only if A! is. The last statement implies that a certain Calabi-Yau property is preserved under Koszul duality.


The first author is supported by the NSFC (project 10571152) of China and the NSF of Zhejiang Province (J20080154). The third author is supported by the NSFC (key project 10331030) of China and Doctorate Foundation (No. 20060246003), Ministry of Education of China. The fourth author is supported by the NSF of USA and the Royalty Research Fund of the University of Washington.

Author information

Di Ming Lu:
Department of Mathematics, Zhejiang University, Hangzhou 310027, China

John H. Palmieri:
Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195, USA

Quan Shui Wu:
Institute of Mathematics, Fudan University, Shanghai, 200433, China

James J. Zhang:
Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195, USA