Left invariant flat projective structures on Lie groups and prehomogeneous vector spaces
Use this link to cite this item : https://ir.lib.hiroshima-u.ac.jp/00031748
ID | 31748 |
file | |
title alternative | リー群上の左不変平坦な射影構造と概均質ベクトル空間
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creator |
Hironao, Kato
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subject | left invariant flat projective structure
prehomogeneous vector space
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NDC |
Mathematics
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abstract | We show the correspondence between left invariant flat projective structures on Lie groups and certain prehomogeneous vector spaces. Moreover by using the classification theory of prehomogeneous vector spaces, we classify complex Lie groups admitting irreducible left invariant flat complex projective structures. As a result, direct sums of special linear Lie algebras sl(2) ⊕ sl(m_1) ⊕ ⋅ ⋅ ⋅ ⊕ sl(m_k) admit left invariant flat complex projective structures if the equality 4 + m^2_1 + ⋅ ⋅ ⋅ + m^2_k - k - 4m_1m_2 ⋅ ⋅ ⋅ m_k = 0 holds. These contain sl(2), sl(2) ⊕ sl(3), sl(2) ⊕ sl(3) ⊕ sl(11) for example.
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language |
eng
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nii type |
Thesis or Dissertation
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HU type |
Doctoral Theses
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DCMI type | text
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format | application/pdf
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rights | Copyright(c) by Author
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grantid | 甲第5461号
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degreeGrantor | 広島大学(Hiroshima University)
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degreename Ja | 博士(理学)
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degreename En | Physical Science
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degreelevel | doctoral
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date of granted | 2011-03-23
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department |
Graduate School of Science
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