Left invariant flat projective structures on Lie groups and prehomogeneous vector spaces
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| File | |
| Title ( eng ) |
Left invariant flat projective structures on Lie groups and prehomogeneous vector spaces
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| Title ( jpn ) |
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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| 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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| Keywords |
left invariant flat projective structure
prehomogeneous vector space
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| NDC |
Mathematics [ 410 ]
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| Language |
eng
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| Resource Type | doctoral thesis |
| Rights |
Copyright(c) by Author
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| Access Rights | open access |
| Dissertation Number | 甲第5461号 |
| Degree Name | |
| Date of Granted | 2011-03-23 |
| Degree Grantors |
広島大学
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