PROJECTIVE GEOMETRY OF FREUDENTHAL'S VARIETIES OF CERTAIN TYPE
PROJECTIVE GEOMETRY OF FREUDENTHAL'S VARIETIES OF CERTAIN TYPE
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DOI：
10.1307/mmj/1100623411
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发表时间：
2004-12
影响因子：
0.9
通讯作者：
Hajime Kaji;Osami Yasukura
中科院分区：
文献类型：
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作者：
Hajime Kaji;Osami Yasukura
H.弗赖登塔尔在他的一系列论文中（见[10]及其参考文献），通过定义各种投射簇，构造了E8、E7、E6和F4型的例外李代数。我们工作的目的是研究射影几何的某些类型的品种，这是所谓的品种的飞机在辛几何的弗赖登塔尔（见[10，4.11]，[22，2.3]）。设g是复数域C上的分次单有限维李代数，其阶数介于−2和2之间，dim g2 = 1，g1=/ 0，即接触型分次李代数：g = g−2 <$g−1 <$g0 <$g1 <$g2（参见§1）。设V：= {x ∈ g1 \ {0}|（adx）g−2 = 0}，
H. Freudenthal constructed, in a series of his papers (see [10] and its references), the exceptional Lie algebras of type E8, E7, E6 and F4, with defining various projective varieties. The purpose of our work is to study projective geometry for his varieties of certain type, which are called varieties of planes in the symplectic geometry of Freudenthal (see [10, 4.11], [22, 2.3]). Let g be a graded, simple, finite-dimensional Lie algebra over the complex number field C with grades between −2 and 2, dim g2 = 1 and g1=/ 0, namely a graded Lie algebra of contact type: g = g−2 ⊕ g−1 ⊕ g0 ⊕ g1 ⊕ g2 (see §1). We set V := {x ∈ g1 \ {0}|(adx)g−2 = 0},