Tilting and trivial extensions |
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Authors: | Qinghua Chen Meiyong Gong Wolfgang Rump |
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Institution: | 1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, China 2. Institute for Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70550, Stuttgart, Germany
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Abstract: | The trivial extensions of a quasi-abelian category by means of a fully exact endofunctor are again quasi-abelian. Using the
one-to-one correspondence between quasi-abelian categories and tiltings, it is shown that the trivial extension of a quasi-abelian
category corresponds to a trivial extension of the associated tilting. As an application, a criterion for tilting modules
over an arbitrary ring R to be liftable to a tilting module over a trivial extension ring
R\ltimes M{R\ltimes M} is given. |
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Keywords: | |
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