DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Choi, Suh-Young | - |
dc.contributor.advisor | 최서영 | - |
dc.contributor.author | Choi, Kang-Hyun | - |
dc.contributor.author | 최강현 | - |
dc.date.accessioned | 2013-09-12T02:32:06Z | - |
dc.date.available | 2013-09-12T02:32:06Z | - |
dc.date.issued | 2013 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=513604&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/181548 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2013.2, [ iii, 25 p. ] | - |
dc.description.abstract | In this paper, we prove the criterion for a Zariski dense subgroup generated by reflections $\Gamma \subset \SL^{\pm}(n+1,\mathbb{R})$ to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in the field $\mathbb{R}$. We apply this criterion for groups generated by reflections that act cocompactly on irreducible properly convex open subdomains of the $n$-dimensional projective sphere. This gives a methodology to construct injective group homomorphisms from such Coxeter groups to $\SL^{\pm}(n+1,\mathbb{Z})$. Finally we provide some examples of $\SL^{\pm}(n+1,\mathbb{Z})$-representations of such Coxeter groups. In particular, we consider simplicial reflection groups that are isomorphic to hyperbolic simplicial groups and classify all the conjugacy classes of the reflection subgroups in $\SL^{\pm}(n+1,\mathbb{R})$ that are definable over $\mathbb{Z}$. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Coxeter group | - |
dc.subject | reflection group | - |
dc.subject | ring of definition | - |
dc.subject | 콕세터군 | - |
dc.subject | 반사군 | - |
dc.subject | 정의되는 환 | - |
dc.subject | 실사영구조 | - |
dc.subject | real projective structure | - |
dc.title | The definability criterion for cocompact convex projective polyhedral reflection groups | - |
dc.title.alternative | Cocompact한 볼록사영 다면체 반사군의 정의가능성 판단기준 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 513604/325007 | - |
dc.description.department | 한국과학기술원 : 수리과학과, | - |
dc.identifier.uid | 020085338 | - |
dc.contributor.localauthor | Choi, Suh-Young | - |
dc.contributor.localauthor | 최서영 | - |
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