From triangulated categories to abelian categories--cluster tilting in a general framework

Details From triangulated categories to abelian categories--cluster tilting in a general framework From triangulated categories to abelian categories--cluster tilting in a general framework

2006-05-03

arxiv.org/abs/math/0605100v3

Mathematics

Representation Theory

final version, to appear in Math. Z. minor changes

Scientific paper

We put cluster tilting in ageneral framework by showing that any quotient of
a triangulated category modulo a tilting subcategory (that is, a maximal
one-orthogonal subcategory) carries an abelian structure. These abelian
quotients turn out to be module categories of Goreisten algebras of dimension
at most one.

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