A category equivalence between homogeneous completely decomposable abelian groups and modules over principal ideal domains
✍ Scribed by Lutz Strüengmann
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 91 KB
- Volume
- 159
- Category
- Article
- ISSN
- 0022-4049
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✦ Synopsis
Let Z ⊆ R be a subgroup of the rationals and (S; ≤) a ÿnite poset. In this paper we introduce the category Rep(S; R) of homogeneous completely decomposable groups H of type R with distinguished homogeneous completely decomposable subgroups H i (i ∈ S) of the same type, respecting the order of S, i.e. if i; j ∈ S and i ≤ j, then H i ⊆ H j . We construct a category equivalence between the two categories Rep(S; R) and Rep(S; R0), where R0 =End(R). Using this equivalence we are able to obtain decomposition theorems for certain subclasses of Rep 2 (R) and Rep 3 (R). We prove that these special representations admit a decomposition into indecomposable representations of rank ≤ 2.