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dc.contributor.authorBolsinov, Alexey V.
dc.contributor.authorKonyaev, Andrey Yu.
dc.contributor.authorMatveev, Vladimir S.
dc.date.accessioned2022-02-01T07:38:34Z
dc.date.available2022-02-01T07:38:34Z
dc.date.issued2022-01-20
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3915
dc.description.abstractWe consider multicomponent local Poisson structures of the form $\mathcal P_3 + \mathcal P_1$, under the assumption that the third order term $\mathcal P_3$ is Darboux-Poisson and non-degenerate, and study the Poisson compatibility of two such structures. We give an algebraic interpretation of this problem in terms of Frobenius algebras and reduce it to classification of Frobenius pencils, i.e. of linear families of Frobenius algebras. Then, we completely describe and classify Frobenius pencils under minor genericity conditions. In particular we show that each such Frobenuis pencil is a subpencil of a certain ${\it maximal}$ pencil. These maximal pencils are uniquely determined by some combinatorial object, a directed rooted in-forest with vertices labeled by natural numbers whose sum is the dimension of the manifold. These pencils are naturally related to certain (polynomial, in the most nondegenerate case) pencils of Nijenhuis operators. We show that common Frobenius coordinate systems admit an elegant invariant description in terms of the Nijenhuis pencil.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2022-01
dc.titleApplications of Nijenhuis Geometry III: Frobenius Pencils and Compatible Non-Homogeneous Poisson Structuresen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2022-01
local.scientificprogramOWRF 2021en_US
local.series.idOWP-2022-01en_US
local.subject.msc37en_US
local.subject.msc53en_US
dc.identifier.urnurn:nbn:de:101:1-2022030212050119970561
dc.identifier.ppn1794979190


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