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| Koszul Differential Graded Algebras and BGG Correspondence II |
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Citation： |
Jiwei HE,Quanshui WU.Koszul Differential Graded Algebras and BGG Correspondence II[J].Chinese Annals of Mathematics B,2010,31(1):133~144 |
| Page view： 2039
Net amount： 1546 |
Authors： |
Jiwei HE; Quanshui WU; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10801099, 10731070)
and the Doctoral Program Foundation of the Ministry of Education of China (No. 20060246003). |
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| Abstract： |
The concept of Koszul differential graded (DG for short) algebra is introduced
in [8]. Let A be a Koszul DG algebra. If the Ext-algebra of A is finite-dimensional, i.e.,
the trivial module Ak is a compact object in the derived category of DG A-modules, then
it is shown in [8] that A has many nice properties. However, if the Ext-algebra is infinite-
dimensional, little is known about A. As shown in [15] (see also Proposition 2.2), Ak is not
compact if H(A) is finite-dimensional. In this paper, it is proved that the Koszul duality
theorem also holds when H(A) is finite-dimensional by using Foxby duality. A DG version
of the BGG correspondence is deduced from the Koszul duality theorem. |
Keywords： |
Koszul differential graded algebra, Koszul duality, BGG correspondence |
Classification： |
16E05, 16E40, 16W50 |
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