DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 백상훈 | - |
dc.contributor.author | Kim, Yeongjong | - |
dc.contributor.author | 김영종 | - |
dc.date.accessioned | 2024-08-08T19:31:19Z | - |
dc.date.available | 2024-08-08T19:31:19Z | - |
dc.date.issued | 2024 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=1099296&flag=dissertation | en_US |
dc.identifier.uri | http://hdl.handle.net/10203/322077 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2024.2,[iii, 49 p. :] | - |
dc.description.abstract | In this paper, we present the essential dimension of reductive groups. We propose a method to construct generically free representations of split reductive groups with finite or connected center, which gives upper bounds on the essential dimension of those groups. Combining our upper bound with previously known lower bound, we give the exact value of the essential dimension of some types of reductive groups. As an application, we determine the essential dimension of a semisimple group of classical type or E6, and its strict reductive envelope under certain conditions on its center. Among these, the result on groups of type B and D has an application to quadratic forms. We also give the essential dimension of some semisimple groups of type B for which we cannot apply our method using generically free representation. | - |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Essential dimension▼aTorsor▼a가약군▼a반단순군▼a일반적 자유 표현▼a갈루아 코호몰로지▼a이차형식 | - |
dc.subject | Essential dimension▼aTorsor▼aReductive group▼aSemisimple group▼aGenerically free representation▼aGalois cohomology▼aQuadratic form | - |
dc.title | Essential dimension of reductive groups | - |
dc.title.alternative | 가약군의 essential dimension | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 325007 | - |
dc.description.department | 한국과학기술원 :수리과학과, | - |
dc.contributor.alternativeauthor | Baek, Sanghoon | - |
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