Adjoint functors, projectivization, and differentiation algorithms for representations of partially ordered sets

Kleiner, Mark; Reitenbach, Markus

doi:10.1016/j.jalgebra.2011.12.018

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Lemma 23 Assume S Is a Forest1

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2016

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“…The next lemma is used in the proof of Theorem I. Part (a) of the lemma is well known for representations over fields as part of a more elaborate theory involving adjoint functors ( [13]). Part (b) has no analogue for fields.…”

Section: Lemma 23 Assume S Is a Forestmentioning

confidence: 99%

Representations of finite posets over the ring of integers modulo a prime power

Arnold¹,

Mader²,

Mutzbauer³

et al. 2016

J. Commut. Algebra

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The classical category Rep(S, Zp) of representations of a finite poset S over the field Zp is extended to two categories, Rep(S, Z p m ) and uRep(S, Z p m ), of representations of S over the ring Z p m . A list of values of S and m for which Rep(S, Z p m ) or uRep(S, Z p m ) has infinite representation type is given for the case that S is a forest. Applications include a computation of the representation type for certain classes of abelian groups, as the category of sincere representations in (uRep(S, Z p m )) Rep(S, Z p m ) has the same representation type as (homocyclic) (S, p m )-groups, a class of almost completely decomposable groups of finite rank. On the other hand, numerous known lists of examples of indecomposable (S, p m )-groups give rise to lists of indecomposable representations.

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Section: Lemma 23 Assume S Is a Forestmentioning

confidence: 99%