Mazorchuk, V. (2002) Enright's completions and injectively copresented modules. Transactions of the American Mathematical Society, 7(354), pp. 2725-2743.
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Abstract
Let A be a nite-dimensional simple Lie algebra over the complex numbers. It is shown that a module is complete (or relatively complete) in the sense of Enright if and only if it is injectively copresented by certain injective modules in the BGG-category O.L etA be the nite-dimensional algebra associated to a block ofO. Then the corresponding block of the category of complete modules is equivalent to the category of eAe-modules for a suitable choice of the idempotente. Using this equivalence, a very easy proof is given for Deodhar's theorem (also proved by Bouaziz) that completion functors satisfy braid relations. The algebra eAe is left properly and standardly stratied. It satises a double centralizer property similar to Soergel's \combinatorial description" ofO. Its simple objects, their characters and their multiplicities in projective or standard objects are determined.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Mazorchuk, Dr Volodymyr |
Authors: | Mazorchuk, V. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Transactions of the American Mathematical Society |
Publisher: | American Mathematical Society |
ISSN: | 0002-9947 |
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