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dc.contributor.author김선영-
dc.date.accessioned2020-12-10T16:30:10Z-
dc.date.available2020-12-10T16:30:10Z-
dc.date.issued2020-
dc.identifier.issn0016-2736-
dc.identifier.issn1730-6329-
dc.identifier.otherOAK-28082-
dc.identifier.urihttps://dspace.ewha.ac.kr/handle/2015.oak/255684-
dc.description.abstractGiven an arbitrary connected groupoid G with its vertex group G(a), if G(a) is a central subgroup of a group F, then there is a canonical extension F = G circle times F of G in the sense that Ob(G) = Ob(F), Mor(G) subset of Mor(F), and F is isomorphic to all the vertex groups of F. From the failure of 3-uniqueness of a strong type p over A = acl(eq)(A) in a stable theory T, a canonical finitary connected commutative groupoid G with the binding group G was A-type-definably constructed by John Goodrick and Alexei Kolesnikov (2012). In this paper we take a certain (possibly non-commutative) automorphism group F where G is embedded centrally (so inducing t(a) : G(a) -> Z(F)), and show that the abstract groupoid G circle times F lives A-invariantly in models of T. More precisely, we A-invariantly construct a connected groupoid T, isomorphic to G circle times F as abstract groupoids, satisfying the following: (1) Ob(F) = Ob(G), and Mor(F) and composition maps are A-invariant (i.e., described by infinite disjunctions of conjunctions of formulas over A), so that an A-automor-phism of a model of T induces a groupoid automorphism of F. (2) There is an A-invariant faithful functor I : G -> F which is the identity on the objects, and I(G(a)) = i(a) o t(a), where i(a) is a canonical group isomorphism from F onto a vertex group F-a of F. An automorphism group approximated by the vertex groups of the non-commutative groupoids is suggested as a "fundamental group" of the strong type p.-
dc.languageEnglish-
dc.publisherPOLISH ACAD SCIENCES INST MATHEMATICS-IMPAN-
dc.subjectgeneric groupoid-
dc.subject3-uniqueness-
dc.subjectfundamental group-
dc.titleNon-commutative groupoids obtained from the failure of 3-uniqueness in stable theories-
dc.typeArticle-
dc.relation.issue1-
dc.relation.volume249-
dc.relation.indexSCIE-
dc.relation.indexSCOPUS-
dc.relation.startpage47-
dc.relation.lastpage70-
dc.relation.journaltitleFUNDAMENTA MATHEMATICAE-
dc.identifier.doi10.4064/fm755-7-2019-
dc.identifier.wosidWOS:000561708000004-
dc.author.googleKim, Byunghan-
dc.author.googleKim, SunYoung-
dc.author.googleLee, Junguk-
dc.contributor.scopusid김선영(57221275622)-
dc.date.modifydate20210915112050-
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자연과학대학 > 수학전공 > Journal papers
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