dc.contributor.author Bolsinov, Alexey V. dc.contributor.author Konyaev, Andrey Yu. dc.contributor.author Matveev, Vladimir S. dc.date.accessioned 2022-02-01T07:38:34Z dc.date.available 2022-02-01T07:38:34Z dc.date.issued 2022-01-20 dc.identifier.uri http://publications.mfo.de/handle/mfo/3915 dc.description.abstract We 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 en_US systems admit an elegant invariant description in terms of the Nijenhuis pencil. dc.language.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2022-01 dc.title Applications of Nijenhuis Geometry III: Frobenius Pencils and Compatible Non-Homogeneous Poisson Structures en_US dc.type Preprint en_US dc.rights.license Dieses 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.license This 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.doi 10.14760/OWP-2022-01 local.scientificprogram OWRF 2021 en_US local.series.id OWP-2022-01 en_US local.subject.msc 37 en_US local.subject.msc 53 en_US dc.identifier.urn urn:nbn:de:101:1-2022030212050119970561 dc.identifier.ppn 1794979190
﻿