Left invariant flat projective structures on Lie groups and prehomogeneous vector spaces

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

加藤 宏尚

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.

left invariant flat projective structure

prehomogeneous vector space

数学 [ 410 ]

英語

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広島大学