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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Generalised Moore spectra in a triangulated category
AU - Pauksztello, David
PY - 2010/11
Y1 - 2010/11
N2 - In this paper we consider a construction in an arbitrary triangulated category TT which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of TT satisfying some finite tilting assumptions, we obtain a functor which “approximates” objects from the module category of the endomorphism algebra of C in TT . This provides a higher analogue of a construction of Jørgensen which appears in (Manuscr Math 110:381–406, 2003) in connection with lifts of certain homological functors of derived categories. We show that this new functor is well-behaved with respect to short exact sequences and distinguished triangles, and as a consequence we obtain a new way of embedding a module category in a triangulated category. As an example of the theory, we recover Keller’s canonical embedding of the module category of a path algebra of a quiver with no oriented cycles into its u-cluster category of u⩾2u⩾2 .
AB - In this paper we consider a construction in an arbitrary triangulated category TT which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of TT satisfying some finite tilting assumptions, we obtain a functor which “approximates” objects from the module category of the endomorphism algebra of C in TT . This provides a higher analogue of a construction of Jørgensen which appears in (Manuscr Math 110:381–406, 2003) in connection with lifts of certain homological functors of derived categories. We show that this new functor is well-behaved with respect to short exact sequences and distinguished triangles, and as a consequence we obtain a new way of embedding a module category in a triangulated category. As an example of the theory, we recover Keller’s canonical embedding of the module category of a path algebra of a quiver with no oriented cycles into its u-cluster category of u⩾2u⩾2 .
U2 - 10.1007/s00229-010-0374-0
DO - 10.1007/s00229-010-0374-0
M3 - Journal article
VL - 133
SP - 347
EP - 372
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 3-4
ER -