Matches in SemOpenAlex for { <https://semopenalex.org/work/W4289801145> ?p ?o ?g. }
Showing items 1 to 55 of
55
with 100 items per page.
- W4289801145 abstract "In the paper Pappus's theorem and the modular group, R. Schwartz constructed a 2-dimensional family of faithful representations $rho_Theta$ of the modular group $mathrm{PSL}(2,mathbb{Z})$ into the group $mathscr{G}$ of projective symmetries of the projective plane via Pappus Theorem. The image of the unique index 2 subgroup $mathrm{PSL}(2,mathbb{Z})_o$ of $mathrm{PSL}(2,mathbb{Z})$ under each representation $rho_Theta$ is in the subgroup $mathrm{PGL}(3,mathbb{R})$ of $mathscr{G}$ and preserves a topological circle in the flag variety, but $rho_Theta$ is not Anosov. In her PhD Thesis, V. P. Val'erio elucidated the Anosov-like feature of Schwartz representations: For every $rho_Theta$, there exists a 1-dimensional family of Anosov representations $rho^varepsilon_{Theta}$ of $mathrm{PSL}(2,mathbb{Z})_o$ into $mathrm{PGL}(3,mathbb{R})$ whose limit is the restriction of $rho_Theta$ to $mathrm{PSL}(2,mathbb{Z})_o$. In this paper, we improve her work: For each $rho_Theta$, we build a 2-dimensional family of Anosov representations of $mathrm{PSL}(2,mathbb{Z})_o$ into $mathrm{PGL}(3,mathbb{R})$ containing $rho^varepsilon_{Theta}$ and a 1-dimensional subfamily of which can extend to representations of $mathrm{PSL}(2,mathbb{Z})$ into $mathscr{G}$. Schwartz representations are therefore, in a sense, the limits of Anosov representations of $mathrm{PSL}(2,mathbb{Z})$ into $mathscr{G}$." @default.
- W4289801145 created "2022-08-05" @default.
- W4289801145 creator A5004276299 @default.
- W4289801145 creator A5012129322 @default.
- W4289801145 creator A5071567822 @default.
- W4289801145 date "2018-01-25" @default.
- W4289801145 modified "2023-10-16" @default.
- W4289801145 title "Pappus Theorem, Schwartz Representations and Anosov Representations" @default.
- W4289801145 hasPublicationYear "2018" @default.
- W4289801145 type Work @default.
- W4289801145 citedByCount "0" @default.
- W4289801145 crossrefType "journal-article" @default.
- W4289801145 hasAuthorship W4289801145A5004276299 @default.
- W4289801145 hasAuthorship W4289801145A5012129322 @default.
- W4289801145 hasAuthorship W4289801145A5071567822 @default.
- W4289801145 hasBestOaLocation W42898011451 @default.
- W4289801145 hasConcept C10464949 @default.
- W4289801145 hasConcept C114614502 @default.
- W4289801145 hasConcept C115961682 @default.
- W4289801145 hasConcept C121332964 @default.
- W4289801145 hasConcept C154945302 @default.
- W4289801145 hasConcept C181633103 @default.
- W4289801145 hasConcept C2781311116 @default.
- W4289801145 hasConcept C33923547 @default.
- W4289801145 hasConcept C41008148 @default.
- W4289801145 hasConcept C62520636 @default.
- W4289801145 hasConceptScore W4289801145C10464949 @default.
- W4289801145 hasConceptScore W4289801145C114614502 @default.
- W4289801145 hasConceptScore W4289801145C115961682 @default.
- W4289801145 hasConceptScore W4289801145C121332964 @default.
- W4289801145 hasConceptScore W4289801145C154945302 @default.
- W4289801145 hasConceptScore W4289801145C181633103 @default.
- W4289801145 hasConceptScore W4289801145C2781311116 @default.
- W4289801145 hasConceptScore W4289801145C33923547 @default.
- W4289801145 hasConceptScore W4289801145C41008148 @default.
- W4289801145 hasConceptScore W4289801145C62520636 @default.
- W4289801145 hasLocation W42898011451 @default.
- W4289801145 hasLocation W42898011452 @default.
- W4289801145 hasLocation W42898011453 @default.
- W4289801145 hasLocation W42898011454 @default.
- W4289801145 hasOpenAccess W4289801145 @default.
- W4289801145 hasPrimaryLocation W42898011451 @default.
- W4289801145 hasRelatedWork W1978042415 @default.
- W4289801145 hasRelatedWork W1986391854 @default.
- W4289801145 hasRelatedWork W2017331178 @default.
- W4289801145 hasRelatedWork W2047138652 @default.
- W4289801145 hasRelatedWork W2070120468 @default.
- W4289801145 hasRelatedWork W2134386818 @default.
- W4289801145 hasRelatedWork W2269408135 @default.
- W4289801145 hasRelatedWork W2952024992 @default.
- W4289801145 hasRelatedWork W2976797620 @default.
- W4289801145 hasRelatedWork W3086542228 @default.
- W4289801145 isParatext "false" @default.
- W4289801145 isRetracted "false" @default.
- W4289801145 workType "article" @default.