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Bulletin of the London Mathematical Society Advance Access originally published online on September 4, 2008
Bulletin of the London Mathematical Society 2008 40(6):985-994; doi:10.1112/blms/bdn080
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© 2008 London Mathematical Society

A counterexample to Raikov's conjecture

Wolfgang Rump

Institute for Algebra and Number Theory
University of Stuttgart
Pfaffenwaldring 57
D-70550 Stuttgart
Germany

Received 4 January 2008. Revision received 18 June 2008.

Quasi-abelian categories are additive categories for which the class of all short exact sequences defines an exact structure. Such categories are ubiquitous and form a natural framework for relative homological algebra and K-theory. Higher Ext-groups also exist in categories with the formally weaker property to be semi-abelian. Raikov's conjecture states that both concepts are equivalent. We use a tilted algebra of type E6 to construct a counterexample.

Dedicated to B.V.M.

2000 Mathematics Subject Classification 18E10, 18G25, 16D90 (primary), 16G10, 16G70 (secondary).


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