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dc.contributor.authorBate, Michael
dc.contributor.authorMartin, Benjamin
dc.contributor.authorRöhrle, Gerhard
dc.date.accessioned2023-06-19T10:29:10Z
dc.date.available2023-06-19T10:29:10Z
dc.date.issued2023-06-19
dc.identifier.urihttp://publications.mfo.de/handle/mfo/4041
dc.description.abstractGiven a semisimple linear algebraic $k$-group $G$, one has a spherical building $Δ_G$, and one can interpret the geometric realisation $Δ_G(\mathbb R)$ of $Δ_G$ in terms of cocharacters of $G$. The aim of this paper is to extend this construction to the case when $G$ is an arbitrary connected linear algebraic group; we call the resulting object $Δ_G(\mathbb R)$ the spherical edifice of $G$. We also define an object $V_G(\mathbb R)$ which is an analogue of the vector building for a semisimple group; we call $V_G(\mathbb R)$ the vector edifice. The notions of a linear map and an isomorphism between edifices are introduced; we construct some linear maps arising from natural group-theoretic operations. We also devise a family of metrics on $V_G(\mathbb R)$ and show they are all bi-Lipschitz equivalent to each other; with this extra structure, $V_G(\mathbb R)$ becomes a complete metric space. Finally, we present some motivation in terms of geometric invariant theory and variations on the Tits Centre Conjecture.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2023-04
dc.subjectSpherical buildings
dc.subjectEdifices
dc.subjectTits Centre Conjecture
dc.subjectGeometric invariant theory
dc.titleEdifices: Building-like Spaces Associated to Linear Algebraic Groups; In memory of Jacques Titsen_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-2023-04
local.scientificprogramOWRF 2023en_US
local.series.idOWP-2023-04en_US
local.subject.msc51en_US
local.subject.msc20en_US
dc.identifier.ppn1851039716


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