A counterexample to Raikov's conjecture | Zendy

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A counterexample to Raikov's conjecture

Author(s) -

Rump Wolfgang

Publication year - 2008

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/bdn080

Subject(s) - counterexample , mathematics , conjecture , abelian group , construct (python library) , pure mathematics , class (philosophy) , property (philosophy) , type (biology) , algebra over a field , discrete mathematics , computer science , epistemology , artificial intelligence , ecology , philosophy , biology , programming language

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 6 to construct a counterexample.

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