ISSN:
1420-9020
Keywords:
Key words. $ ({\frak g}, K) $-modules, Cohen-Macaulay categories, Grothendieck duality.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. Let $ ({\frak g}, K) $ be a Harish-Chandra pair. In this paper we prove that if P and P' are two projective $ ({\frak g}, K) $ -modules, then Hom(P, P') is a Cohen-Macaulay module over the algebra $ {\cal Z}({\frak g}, K) $ of K-invariant elements in the center of $ U({\frak g}) $ . This fact implies that the category of $ ({\frak g}, K) $ -modules is locally equivalent to the category of modules over a Cohen-Macaulay algebra, where by a Cohen-Macaulay algebra we mean an associative algebra that is a free finitely generated module over a polynomial subalgebra of its center.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s000290050012
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